Algebraic K-theory and its applications
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| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1996
|
| Ausgabe: | Corr. 2. printing |
| Schriftenreihe: | Graduate texts in mathematics
147 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Rosenberg, Jonathan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Algebraic K-theory and its applications |c Jonathan Rosenberg |
| 250 | |a Corr. 2. printing | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1996 | |
| 300 | |a X, 392 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 147 | |
| 650 | 4 | |a K-theory | |
| 650 | 0 | 7 | |a Algebraische K-Theorie |0 (DE-588)4141839-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Algebraische K-Theorie |0 (DE-588)4141839-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Graduate texts in mathematics |v 147 |w (DE-604)BV000000067 |9 147 | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0002 MAT 552f 77 A 3300 |
|---|---|
| DE-BY-TUM_katkey | 879413 |
| DE-BY-TUM_location | 00 |
| DE-BY-TUM_media_number | 040003941104 |
| _version_ | 1820874683287863296 |
| adam_text | Contents
Preface
Chapter
1.
Ko
oí Rings
1
1.
Defining
Ко
1
2.
Ko
from idempotents
7
3.
Ko
of
РШв
aud local
rings
11
4.
Ko
of Dedekind domains
16
5.
Relative
Ko
and excision
27
6.
An application: Swan s Theorem and
topologicei
К-
theory
32
7.
Another application:
Euler
characteristics and the Wall
ñniteness
obstruction
41
Chapter
2.
Ki of Rings
59
1.
Defining
ΑΊ
59
2.
K of division rings and local rings
62
3.
K of
РШѕ
and Dedekind domains
74
4.
Whitehead groups and Whitehead torsion
83
5.
Relative K and the exact sequence
92
Chapter
3.
Ко
and
ΑΊ
of Categories, Negative
Ä-Theory
108
1.
Kq and
Κι
of categories, Gq and G of rings
108
2.
The Grothendieck and Bass-Heller-Swan Theorems
132
3.
Negative Jf-theory
153
Chapter
4.
Milnor s K2
162
1.
Universal central extensions and
Щ
162
Universal central extensions
163
Homology of groups
168
2.
The Steinberg group
187
3.
Milnor s
Kt
199
4.
Applications of Ki
218
Computing certain relative
Κ χ
groups
218
Ki of fields and number theory
221
Almost commuting operators
237
Pseudo-isotopy
240
χ
Contents
Chapter
5.
The
+-
Construction and Quillen
iC-Theory
245
1.
An introduction to classifying spaces
245
2.
Quillen s +4;onstruction and its basic properties
265
3.
A survey of higher K-theary
279
Products
279
Jr-theory of fields and of rings of integers
281
The Q-construction and results proved with it
289
Applications
295
Chapter
6.
Cyclic homology and its relation to
tf-Theory
302
1.
Basics of cyclic homology
302
Hochschild
homology
302
Cyclic homology
306
Connections with non-commutative
de Rham
theory
325
2.
The Chern character
331
The classical Chern character
332
The Chern character on Ko
335
The Chern character on higher K-theory
340
3.
Some applications
350
Non-vanishing of class groups and Whitehead groups
350
Idempotents in C^algebras
355
Group rings and assembly maps
362
References
369
Books and Monographs on Related Areas of Algebra,
Analysis, Number Theory, and Topology
369
Books and Monographs on Algebraic if-Theory
371
Specialized References
372
Notational Index
377
Subject Index
383
|
| any_adam_object | 1 |
| author | Rosenberg, Jonathan |
| author_facet | Rosenberg, Jonathan |
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| callnumber-sort | QA 3612.33 R67 41994 |
| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 552f |
| ctrlnum | (OCoLC)34321821 (DE-599)BVBBV011116957 |
| dewey-full | 512/.55 512/.5520 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-search | 512/.55 512/.55 20 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Corr. 2. printing |
| format | Book |
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| id | DE-604.BV011116957 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T14:23:47Z |
| institution | BVB |
| isbn | 3540942483 0387942483 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007449561 |
| oclc_num | 34321821 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-91 DE-BY-TUM DE-384 DE-521 DE-11 DE-188 DE-19 DE-BY-UBM |
| owner_facet | DE-355 DE-BY-UBR DE-91 DE-BY-TUM DE-384 DE-521 DE-11 DE-188 DE-19 DE-BY-UBM |
| physical | X, 392 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spellingShingle | Rosenberg, Jonathan Algebraic K-theory and its applications Graduate texts in mathematics K-theory Algebraische K-Theorie (DE-588)4141839-6 gnd |
| subject_GND | (DE-588)4141839-6 |
| title | Algebraic K-theory and its applications |
| title_auth | Algebraic K-theory and its applications |
| title_exact_search | Algebraic K-theory and its applications |
| title_full | Algebraic K-theory and its applications Jonathan Rosenberg |
| title_fullStr | Algebraic K-theory and its applications Jonathan Rosenberg |
| title_full_unstemmed | Algebraic K-theory and its applications Jonathan Rosenberg |
| title_short | Algebraic K-theory and its applications |
| title_sort | algebraic k theory and its applications |
| topic | K-theory Algebraische K-Theorie (DE-588)4141839-6 gnd |
| topic_facet | K-theory Algebraische K-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007449561&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT rosenbergjonathan algebraicktheoryanditsapplications |