Combinatorial algebraic topology
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Volume 21 |
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| 100 | 1 | |a Feichtner-Kozlov, Dmitry |d 1972- |0 (DE-588)114514682 |4 aut | |
| 245 | 1 | 0 | |a Combinatorial algebraic topology |c Dmitry Kozlov |
| 264 | 1 | |a Berlin ; Heidelberg ; New York |b Springer |c [2008] | |
| 264 | 4 | |c © 2008 | |
| 300 | |a XIX, 389 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Algorithms and computation in mathematics |v Volume 21 | |
| 650 | 4 | |a Algèbre homologique | |
| 650 | 4 | |a Catégories (Mathématiques) | |
| 650 | 4 | |a Topologie algébrique | |
| 650 | 4 | |a Topologie combinatoire | |
| 650 | 7 | |a Topologie |2 gtt | |
| 650 | 4 | |a Algebra, Homological | |
| 650 | 4 | |a Algebraic topology | |
| 650 | 4 | |a Categories (Mathematics) | |
| 650 | 4 | |a Combinatorial topology | |
| 650 | 0 | 7 | |a Kombinatorische Topologie |0 (DE-588)4137530-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Topologie |0 (DE-588)4120861-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Algebraische Topologie |0 (DE-588)4120861-4 |D s |
| 689 | 0 | 1 | |a Kombinatorische Topologie |0 (DE-588)4137530-0 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Kombinatorische Topologie |0 (DE-588)4137530-0 |D s |
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| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-540-71962-5 |
| 830 | 0 | |a Algorithms and computation in mathematics |v Volume 21 |w (DE-604)BV011131286 |9 21 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015731927&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 550f 2011 A 5065 |
|---|---|
| DE-BY-TUM_katkey | 1775070 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010211162 |
| _version_ | 1820897839779151872 |
| adam_text | Contents
1
Overture
.................................................. 1
Part I Concepts of Algebraic Topology
2
Cell Complexes
............................................ 7
2.1
Abstract Simplicial Complexes
............................ 7
2.1.1
Definition of Abstract Simplicial Complexes and Maps
Between Them
.................................... 7
2.1.2
Deletion, Link, Star, and Wedge
..................... 10
2.1.3
Simplicial Join
.................................... 12
2.1.4
Face Posets
....................................... 12
2.1.5
Barycentric and Stellar Subdivisions
................. 13
2.1.6
Pulling and Pushing Simplicial Structures
............ 15
2.2
Polyhedral Complexes
................................___ 16
2.2.1
Geometry of Abstract Simplicial Complexes
.......... 16
2.2.2
Geometric Meaning of the Combinatorial
Constructions
..................................... 19
2.2.3
Geometric Simplicial Complexes
..................... 23
2.2.4
Complexes Whose Cells Belong to a Specified Set
of Polyhedra
...................................... 25
2.3
Trisps
.................................................. 28
2.3.1
Construction Using the Gluing Data
................. 28
2.3.2
Constructions Involving Trisps
...................... 30
2.4
CW Complexes
......................................... 33
2.4.1
Gluing Along a Map
............................... 33
2.4.2
Constructive and Intrinsic Definitions
................ 34
2.4.3
Properties and Examples
........................... 35
3
Homology Groups
......................................... 37
3.1
Betti
Numbers of Finite Abstract Simplicial Complexes
...... 37
3.2
Simplicial Homology Groups
.............................. 39
XII Contente
3.2.1
Homology
Groups of Trisps with Coefficients in Zg
.... 39
3.2.2
Orientations
...................................... 41
3.2.3 Homolog}
Groups of Trisps with Integer Coefficients
... 41
3.3
Invariants Connected to Homology Groups
.................. 44
3.3.1
Betti
Numbers and Torsion Coefficients
.............. 44
3.3.2
Euler
Characteristic, and the
Euler-Poincaré
Formula
. . 45
3.4
Variations
.............................................. 46
3.4.1
Augmentation and Reduced Homology Groups
........ 46
3.4.2
Homology Groups with Other Coefficients
............ 47
3.4.3
Simplicial Cohomology Groups
...................... 47
3.4.4
Singular Homology
................................ 49
3.5
Chain Complexes
........................................ 51
3.5.1
Definition and Homology of Chain Complexes
......... 51
3.5.2
Maps Between Chain Complexes and Induced Maps
on Homology
..................................... 52
3.5.3
Chain Homotopy
.................................. 53
3.5.4
Simplicial Homology and Cohomology in the Context
of Chain Complexes
............................... 54
3.5.5
Homomorphisms on Homology Induced by Trisp Maps
. 54
3.6
Cellular Homology
....................................... 56
3.6.1
An Application of Homology with Integer Coefficients:
Winding Number
.................................. 56
3.6.2
The Definition of Cellular Homology
................. 57
3.6.3
Cellular Maps and Properties of Cellular Homology
.... 58
4
Concepts of Category Theory
.............................. 59
4.1
The Notion of a Category
................................ 59
4.1.1
Definition of a Category, Isomorphisms
............... 59
4.1.2
Examples of Categories
............................ 60
4.2
Some Structure Theory of Categories
...................... 63
4.2.1
Initial and Terminal Objects
........................ 63
4.2.2
Products and Coproducts
.......................... 64
4.3
Functors
............................................... 68
4.3.1
The Category Cat
................................ 68
4.3.2
Homology and Cohomology Viewed as Functors
....... 70
4.3.3
Group Actions as Functors
......................... 70
4.4
Limit Constructions
..................................... 71
4.4.1
Definition of Colimit of a Functor
................... 71
4.4.2
Colimits and Infinite Unions
........................ 72
4.4.3
Quotients of Group Actions as Colimits
.............. 73
4.4.4
Limits
........................................... 74
4.5
Comma Categories
...................................... 74
4.5.1
Objects Below and Above Other Objects
............. 74
4.5.2
The General Construction and Further Examples
...... 75
Contents XIII
Exact Sequences
........................................... 77
5.1
Some Structure Theory of Long and Short Exact Sequence«
... 77
5.1.1
Construction of the Connecting Homomorphisni
....... 77
5.1.2
Exact Sequences
.................................. 79
5.1.3
Deriving Long Exact Sequences from Short Ones
...... 81
5.2
The Long Exact Sequence of a Pair and Some Applications
... 82
5.2.1
Relative Homology and the
Associated Long
Exact
Sequence
......................................... 82
5.2.2
Applications
...................................... 84
5.3
Mayer-Vietoris Long Exact Sequence
...................... 85
Homotopy
................................................. 89
6.1
Homotopy of Maps
...................................... 89
6.2
Homotopy Type of Topological Spaces
..................... 90
6.3
Mapping Cone and Mapping Cylinder
...................... 91
6.4
Deformation Retracts and Collapses
....................... 93
6.5
Simple Homotopy Type
.................................. 95
6.6
Homotopy Groups
....................................... 96
6.7
Connectivity and Hurewicz Theorem«
...................... 97
Cofibrations
...............................................101
7.1
Cofibrations and the Homotopy Extension Property
..........101
7.2
NDR-Pairs
................ ................. ...........103
7.3
Important Facts Involving Cofibrations
.....................105
7.4
The Relative Homotopy Equivalence
.......................107
Principal P-Bundles and
Stiefel—
Whitney Characteristic
Classes
....................................................
Ill
8.1
Locally Trivial Bundles
...................................
Ill
8.1.1
Bundle Terminology
...............................
Ill
8.1.2
Types of Bundles
..................................112
8.1.3
Bundle Maps
.....................................113
8.2
Elements of the Principal Bundle Theory
...................114
8.2.1
Principal Bundles and Spaces with a Free
Group Action
.....................................114
8.2.2
The Classifying Space of a Group
...................116
8.2.3
Special Cohomology Elements
.......................119
8.2.4
Жг-Ѕрасеѕ
and the Definition
of
Stiefel·
Whitney Classes
..........................120
8.3
Properties of
Stiefel-
Whitney Classes
......................122
8.3.1
Borsuk-
Ulam
Theorem. Index, and Comdex
..........122
8.3.2 Stiefel-Whitney
Height
.............................123
8.3.3
Higher Connectivity and
Stiefel-Whitney
Classes
......123
8.3.4
Combinatorial Construction of
Stiefel
Whitney Classes.
124
8.4
Suggested Reading
.......................................125
XIV Contents
Part II Methods of Combinatorial Algebraic Topology
9
Combinatorial Complexes Melange
........................129
9.1
Abstract Simplicial Complexes
............................129
9.1.1
Simplicial Flag Complexes
..........................129
9.1.2
Order Complexes
..................................130
9.1.3
Complexes of Combinatorial Properties
..............133
9.1.4
The Neighborhood and
Lovász
Complexes
............133
9.1.5
Complexes Arising from Matroids
...................134
9.1.6
Geometric Complexes in
Metric
Spaces
...............134
9.1.7
Combinatorial Presentation by Minimal Nonsimplices
.. 136
9.2
Prodsimplicial Complexes
................................138
9.2.1
Prodsimplicial Flag Complexes
......................138
9.2.2
Complex of Complete Bipartite Subgraphs
............138
9.2.3
Hom
Complexes
...................................140
9.2.4
General Complexes of Morphisms
...................141
9.2.5
Discrete Configuration Spaces of Generalized
Simplicial Complexes
..............................144
9.2.6
The Complex of Phylogenetic Trees
..................144
9.3
Regular Trisps
..........................................145
9.4
Chain Complexes
........................................147
9.5
Bibliographic Notes
......................................148
10
Acyclic Categories
.........................................151
10.1
Basics
..................................................151
10.1.1
The Notion of Acyclic Category
.....................151
10.1.2
Linear Extensions of Acyclic Categories
..............152
10.1.3
Induced Subcategories of Cat
.......................153
10.2
The Regular Trisp of Composable Morphism Chains
in an Acyclic Category
...................................153
10.2.1
Definition and First Examples
......................153
10.2.2
Functoriality
......................................155
10.3
Constructions
...........................................156
10.3.1
Disjoint Union as a Coproduct
......................156
10.3.2
Stacks of Acyclic Categories and Joins
of Regular Trisps
..................................156
10.3.3
Links, Stars, and Deletions
.........................158
10.3.4
Lattices and Acyclic Categories
.....................159
10.3.5
Barycentric Subdivision and Zi-Functor
..............160
10.4
Intervals in Acyclic Categories
............................161
10.4.1
Definition and First Properties
......................161
10.4.2
Acyclic Category of Intervals
and Its Structural Functor
..........................164
10.4.3
Topology of the Category of Intervals
................167
Contents
XV
10.5 Homeomorphisms Associated
with the Direct Product
Construction
............................................168
10.5.1
Simplicial Subdivision of the Direct Product
..........168
10.5.2
Further Subdivisions
...............................171
10.6
The
Möbius
Function
....................................173
10.6.1
Möbius
Function for Posets
.........................173
10.6.2
Möbius
Function for Acyclic Categories
..............174
10.7
Bibliographic Notes
......................................178
11
Discrete Morse Theory
....................................179
11.1
Discrete Morse Theory for Posets
..........................179
11.1.1
Acyclic Matchings in
Hasse
Diagrams of Posets
.......179
11.1.2
Poset
Maps with Small Fibers
......................182
11.1.3
Universal Object Associated to an Acyclic Matching
... 183
11.1.4
Poset
Fibratioiis and the Patchwork Theorem
.........185
11.2
Discrete Morse Theory for
С
W
Complexes
..................187
11.2.1
Attaching Cells to Homotopy Equivalent Spaces
.......187
11.2.2
The Main Theorem of Discrete Morse Theory for CW
Complexes
.......................................189
11.2.3
Examples
........................................192
11.3
Algebraic Morse Theory
..................................201
11.3.1
Acyclic Matchings on Free Chain Complexes
and the Morse Complex
............................201
11.3.2
The Main Theorem of Algebraic Morse Theory
........203
11.3.3
An Example
......................................205
11.4
Bibliographic Notes
......................................208
12
Lexicographic Shellability
..................................211
12.1
Shellability
.............................................211
12.1.1
The Basics
.......................................211
12.1.2
Shelling Induced
Subcomplexes
.....................214
12.1.3
Shelling Nerves of Acyclic Categories
................215
12.2
Lexicographic Shellability
................................216
12.2.1
Labeling Edges as a Way to Order Chains
............216
12.2.2
EL-Labeling
......................................217
12.2.3
General Lexicographic Shellability
...................219
12.2.4
Lexicographic Shellability and Nerves of Acyclic
Categories
........................................223
12.3
Bibliographic Notes
......................................224
13
Evasiveness and Closure Operators
........................225
13.1
Evasiveness
.............................................225
13.1.1
Evasiveness of Graph Properties
.....................225
13.1.2
Evasiveness of Abstract
Siniplicial
Complexes
.........229
XVI Contents
13.2
Closure Operators
.......................................
232
13.2.1
Collapsing Sequences Induced by Closure Operators
. .. 232
13.2.2
Applications
......................................
234
13.2.3
Monotone
Poset
Maps
.............................236
13.2.4
The Reduction Theorem and Implications
............237
13.3
Further Facts About Nonevasiveness
.......................
238
13.3.1
NE-Reduction and Collapses
.........................238
13.3.2
Nonevasiveness of Noncomplemented Lattices
.........240
13.4
Other Recursively Defined Classes of Complexes
.............242
13.5
Bibliographic Notes
......................................243
14
Colimits and Quotients
....................................245
14.1
Quotients of Nerves of Acyclic Categories
...................245
14.1.1
Desirable Properties of the Quotient Construction
.....245
14.1.2
Quotients of Simplicial Actions
......................245
14.2
Formalization of Group Actions and the Main Question
......248
14.2.1
Definition of the Quotient and Formulation
of the Main Problem
...............................248
14.2.2
An Explicit Description of the Category C/G
.........249
14.3
Conditions on Group Actions
.............................250
14.3.1
Outline of the Results and Surjectivity
of the Canonical Map
..............................250
14.3.2
Condition for Injectivity of the Canonical Projection
. .. 251
14.3.3
Conditions for the Canonical Projection
to be an Isomorphism
..............................252
14.3.4
Conditions for the Categories to be Closed
Under Taking Quotients
............................
2oo
14.4
Bibliographic Notes
......................................257
15
Homotopy Colimits
........................................259
15.1
Diagrams over Trisps
....................................259
15.1.1
Diagrams and Colimits
.............................259
15.1.2
Arrow Pictures and Their Nerves
....................260
15.2
Homotopy Colimits
......................................262
15.2.1
Definition and Some Examples
......................262
15.2.2
Structural Maps Associated to Homotopy Colimits
-----263
15.3
Deforming Homotopy Colimits
............................265
15.4
Nerves of Coverings
......................................266
15.4.1
Nerve Diagram
....................................266
15.4.2
Projection Lemma
.................................267
15.4.3
Nerve Lemmas
....................................269
10.5
Gluing Spaces
...........................................271
15.5.1
Gluing Lemma
....................................271
15.5.2
QuiUen Lemma
...................................272
Î5.6
Bibliographic Notes
......................................273
Contents
XVII
16
Spectral Sequences
........................................275
16.1
Filtrations
..............................................275
16.2
Contriving Spectral Sequences
............................276
16.2.1
The Objects to be Constructed
......................276
16.2.2
The Actual Construction
...........................278
16.2.3
Questions of Convergence and Interpretation
of the Answer
.....................................280
16.2.4
An Example
......................................280
16.3
Maps Between Spectral Sequences
.........................281
16.4
Spectral Sequences and Nerves of Acyclic Categories
.........283
16.4.1
A Class of Filtrations
..............................283
16.4.2
Möbius
Function and Inequalities for
Betti
Numbers
.. . 285
16.5
Bibliographic Notes
......................................288
Part III Complexes of Graph Homomorphisms
17
Chromatic Numbers and the Kneser Conjecture
...........293
17.1
The Chromatic Number of a Graph
........................293
17.1.1
The Definition and Applications
.....................293
17.1.2
The Complexity of Computing the Chromatic Number
. 294
17.1.3
The Hadwiger Conjecture
..........................295
17.2
State Graphs and the Variations of the Chromatic Number
... 298
17.2.1
Complete Graphs as State Graphs
...................298
17.2.2
Kneser Graphs as State Graphs and Fractional
Chromatic Number
................................298
17.2.3
The Circular Chromatic Number
....................300
17.3
Kneser Conjecture and
Lovász
Test
........................301
17.3.1
Formulation of the Kneser Conjecture
................301
17.3.2
The Properties of the Neighborhood Complex
.........302
17.3.3
Lovász
Test for Graph Colorings
....................303
17.3.4
Simplicial and Cubical Complexes Associated
to Kneser Graphs
.................................304
17.3.5
The Vertex-Critical Subgraphs of Kneser Graphs
......306
17.3.6
Chromatic Numbers of Kneser Hypergraphs
..........307
17.4
Bibliographic Notes
......................................307
18
Structural Theory of Morphism Complexes
................309
18.1
The Scope of Morphism Complexes
........................309
18.1.1
The Morphism Complexes and the Prodsimplicial
Flag Construction
.................................309
18.1.2
Universality
......................................311
18.2
Special Families of
Hom
Complexes
.........................312
18.2.1
Coloring Complexes of a Graph
.....................312
XVIII
Contents
18.2.2
Complexes
of
Bipartite
Subgraphs and Neighborhood
Complexes
.......................................313
18.3
Functoriality of
Hom
(-, -)................................
315
18.3.1
Functoriality on the Right
..........................315
18.3.2
Aut (G)
Action on Hom(T.G)
.......................316
18.3.3
Functoriality on the Left
...........................316
18.3.4
Aut (T)
Action on
Hom
(Г.
G) .......................
318
18.3.5
Commuting Relations
..............................318
18.4
Products, Compositions, and
Hom
Complexes
...............320
18.4.1
Coproducts
.......................................320
18.4.2
Products
.........................................320
18.4.3
Composition of
Hom
Complexes
.....................322
18.5
Folds
..................................................323
18.5.1
Definition and First Properties
......................323
18.5.2
Proof of the Folding Theorem
.......................324
18.6
Bibliographic Notes
......................................326
19
Characteristic Classes and Chromatic Numbers
............327
19.1
Stiefel
-Whitney Characteristic Classes and Test Graphs
......327
19.1.1
Powers of
Stiefel-
Whitney Classes and Chromatic
Numbers of Graphs
................................327
19.1.2
Stiefel-
Whitney Test Graphs
........................328
19.2
Examples of
Stiefel-Whitney Test
Graphs
..................329
19.2.1
Complexes of Complete Multipartite Subgraphs
.......329
19.2.2
Odd Cycles as
Stiefel-Whitney Test
Graphs
..........334
19.3
Homology Tests for Graph Colorings
.......................337
19.3.1
The Symmetrizer Operator and Related Structures
.... 338
19.3.2
The Topological Rationale for the Tests
..............338
19.3.3
Homology Tests
...................................340
19.3.4
Examples of Homology Tests with Different
Test Graphs
......................................341
19.4
Bibliographic Notes
......................................346
20
Applications of Spectral Sequences to
Hom
Complexes
......349
20.1
НОП1+
Construction
.......................................349
20.1.1
Various Definitions
................................349
20.1.2
Connection to Independence Complexes
..............351
20.1.3
The Support Map
.................................352
20.1.4
An Example: Hom+(Cm, Kn)
........................353
20.2
Setting up the Spectral Sequence
..........................354
20.2.1
Filtration Induced by the Support Map
..............354
20.2.2
The Oth and the
1st
Tableaux
.......................355
20.2.3
The First Differential
..............................355
20.3
Encoding Cohomology Generators by Arc Pictures
...........356
20.3.1
The Language of Arcs
..............................356
20.3.2
The Corresponding Cohomology Generators
..........356
Contents
XIX
20.3.3
The First Reduction
...............................357
20.4
Topology of the Torus Front Complexes
....................358
20.4.1
Reinterpretation of H*{A*t,di) Using a Family
of Cubical Complexes
{Фт,п,д}
......................358
20.4.2
The Torus Front Interpretation
......................360
20.4.3
Grinding
.........................................362
20.4.4
Thin Fronts
......................................364
20.4.5
The Implications for the Cohomology Groups
of
Hom
(Cm, Kn)
...................................366
20.5
Euler
Characteristic Formula
..............................367
20.6
Cohomology with Integer Coefficients
......................368
20.6.1
Fixing Orientations on
Hom
and
Нопц-
Complexes
......368
20.6.2
Signed Versions of
Formula«
for Generators [erf,]
.......370
20.6.3
Completing the Calculation of the Second Tableau
.....371
20.6.4
Summary: the Full Description of the Groups
Я*(Нот(Ст.
A „);Z)...............................
374
20.7
Bibliographic Notes and Conclusion
........................376
References
.....................................................377
Index
..........................................................385
|
| any_adam_object | 1 |
| author | Feichtner-Kozlov, Dmitry 1972- |
| author_GND | (DE-588)114514682 |
| author_facet | Feichtner-Kozlov, Dmitry 1972- |
| author_role | aut |
| author_sort | Feichtner-Kozlov, Dmitry 1972- |
| author_variant | d f k dfk |
| building | Verbundindex |
| bvnumber | BV022525237 |
| callnumber-first | Q - Science |
| callnumber-label | QA169 |
| callnumber-raw | QA169 |
| callnumber-search | QA169 |
| callnumber-sort | QA 3169 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 300 |
| classification_tum | MAT 570f MAT 550f |
| ctrlnum | (OCoLC)185096383 (DE-599)DNB984272755 |
| dewey-full | 512/.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.64 |
| dewey-search | 512/.64 |
| dewey-sort | 3512 264 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV022525237 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T20:07:33Z |
| institution | BVB |
| isbn | 9783540719618 9783540730514 9783540719625 354071961X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015731927 |
| oclc_num | 185096383 |
| open_access_boolean | |
| owner | DE-824 DE-703 DE-355 DE-BY-UBR DE-20 DE-83 DE-11 DE-29T DE-898 DE-BY-UBR DE-91G DE-BY-TUM DE-188 DE-739 |
| owner_facet | DE-824 DE-703 DE-355 DE-BY-UBR DE-20 DE-83 DE-11 DE-29T DE-898 DE-BY-UBR DE-91G DE-BY-TUM DE-188 DE-739 |
| physical | XIX, 389 Seiten Diagramme |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | Algorithms and computation in mathematics |
| series2 | Algorithms and computation in mathematics |
| spellingShingle | Feichtner-Kozlov, Dmitry 1972- Combinatorial algebraic topology Algorithms and computation in mathematics Algèbre homologique Catégories (Mathématiques) Topologie algébrique Topologie combinatoire Topologie gtt Algebra, Homological Algebraic topology Categories (Mathematics) Combinatorial topology Kombinatorische Topologie (DE-588)4137530-0 gnd Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4137530-0 (DE-588)4120861-4 |
| title | Combinatorial algebraic topology |
| title_auth | Combinatorial algebraic topology |
| title_exact_search | Combinatorial algebraic topology |
| title_full | Combinatorial algebraic topology Dmitry Kozlov |
| title_fullStr | Combinatorial algebraic topology Dmitry Kozlov |
| title_full_unstemmed | Combinatorial algebraic topology Dmitry Kozlov |
| title_short | Combinatorial algebraic topology |
| title_sort | combinatorial algebraic topology |
| topic | Algèbre homologique Catégories (Mathématiques) Topologie algébrique Topologie combinatoire Topologie gtt Algebra, Homological Algebraic topology Categories (Mathematics) Combinatorial topology Kombinatorische Topologie (DE-588)4137530-0 gnd Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | Algèbre homologique Catégories (Mathématiques) Topologie algébrique Topologie combinatoire Topologie Algebra, Homological Algebraic topology Categories (Mathematics) Combinatorial topology Kombinatorische Topologie Algebraische Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015731927&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011131286 |
| work_keys_str_mv | AT feichtnerkozlovdmitry combinatorialalgebraictopology |