Characteristic classes of spin surface bundles applications of the Madsen-Weiss theory
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Math. Inst. der Univ.
2006
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| Schriftenreihe: | Bonner mathematische Schriften
381 |
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| 100 | 1 | |a Ebert, Johannes Felix |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Characteristic classes of spin surface bundles |b applications of the Madsen-Weiss theory |c Johannes Felix Ebert |
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Datensatz im Suchindex
| DE-19_call_number | 1601/SI 180-381 |
|---|---|
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| DE-BY-TUM_call_number | 0102 MAT 001z 2001 A 961 |
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| adam_text | Titel: Characteristic classes of spin surface bundles
Autor: Ebert, Johannes Felix
Jahr: 2006
Contents
1 Introduction 6
2 Generalities on surface bundles 15
2.1 Complex structures on surfaces and the diffeomorphism group....... 15
2.2 Surface bundles and bundles of Riemann surfaces.............. 17
2.3 Characteristic classes of surface bundles.................... 18
2.4 The Hodge bundles............................... 20
2.5 Comparison with algebraic geometry..................... 24
3 Spin structures on manifold bundles 27
3.1 Spin structures on vector bundles....................... 27
3.2 Spin structures on manifolds.......................... 29
3.3 Spaces of Spin structures............................ 30
3.4 Spin structures on fiber bundles........................ 34
3.5 When does a smooth fiber bundle have a spin structure?.......... 36
4 Spin structures on surface bundles 38
4.1 Spin structures on surfaces........................... 38
4.2 The spin mapping class group......................... 43
5 Some examples 45
5.1 Finite group actions and the nontriviality of the obstruction class..... 45
5.2 Sphere bundles................................. 47
5.3 Torus bundles.................................. 51
6 The stable homotopy theory of Riemann surfaces 55
6.1 The Becker-Gottlieb-Transfer ......................... 55
6.2 The pushforward................................ 57
6.3 The universal Becker-Gottlieb transfer .................... 58
6.4 Relation to bordism theory........................... 60
6.5 The theorems of Tillmann, Madsen and Weiss................ 62
6.6 Miscellaneous calculations........................... 64
6.7 The Atiyah-Singer index theorem....................... 66
6.8 Examples for the index theorem........................ 67
6.9 From the Mumford conjecture to the Madsen-Tillmann map........ 69
6.10 The Madsen-Tillmann-diagram ........................ 72
7 Divisibility of MMM-classes for spin surface bundles 73
7.1 The general case ................................ 73
7.2 The even classes..............................- - - 74
7.3 The odd classes................................. 74
8 The icosahedral group and ir3(Sr+) 77
8.1 The icosahedral group and the Poincare sphere................ 77
8.2 Surfaces with an action of the icosahedral group............... 78
8.3 Review of the work by Jones-Westbury.................... 81
8.4 Application of the Jones-Westbury formula to the mapping class group . . 82
8.5 Increasing the genus .............................. 84
8.6 Concluding remarks............................... 85
A Appendix on groupoids 86
B List of notations 89
|
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| indexdate | 2025-02-03T17:14:18Z |
| institution | BVB |
| language | English |
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| physical | 94 S. graph. Darst. |
| publishDate | 2006 |
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| publisher | Math. Inst. der Univ. |
| record_format | marc |
| series | Bonner mathematische Schriften |
| series2 | Bonner mathematische Schriften |
| spellingShingle | Ebert, Johannes Felix Characteristic classes of spin surface bundles applications of the Madsen-Weiss theory Bonner mathematische Schriften Homotopy theory Riemann surfaces Spin-Struktur (DE-588)4524559-9 gnd Bündel Mathematik (DE-588)4193459-3 gnd |
| subject_GND | (DE-588)4524559-9 (DE-588)4193459-3 (DE-588)4113937-9 |
| title | Characteristic classes of spin surface bundles applications of the Madsen-Weiss theory |
| title_auth | Characteristic classes of spin surface bundles applications of the Madsen-Weiss theory |
| title_exact_search | Characteristic classes of spin surface bundles applications of the Madsen-Weiss theory |
| title_full | Characteristic classes of spin surface bundles applications of the Madsen-Weiss theory Johannes Felix Ebert |
| title_fullStr | Characteristic classes of spin surface bundles applications of the Madsen-Weiss theory Johannes Felix Ebert |
| title_full_unstemmed | Characteristic classes of spin surface bundles applications of the Madsen-Weiss theory Johannes Felix Ebert |
| title_short | Characteristic classes of spin surface bundles |
| title_sort | characteristic classes of spin surface bundles applications of the madsen weiss theory |
| title_sub | applications of the Madsen-Weiss theory |
| topic | Homotopy theory Riemann surfaces Spin-Struktur (DE-588)4524559-9 gnd Bündel Mathematik (DE-588)4193459-3 gnd |
| topic_facet | Homotopy theory Riemann surfaces Spin-Struktur Bündel Mathematik Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015584088&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001610 |
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