Local and analytic cyclic homology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Zürich
European Math. Soc.
2007
|
| Series: | EMS tracts in mathematics
3 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 360 S. |
| ISBN: | 9783037190395 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface v
Introduction 1
1 Bornological vector spaces and inductive systems 9
1.1 Basic definitions............................ 13
1.2 Some functional analysis....................... 22
1.3 Constructions with bornological vector spaces............ 29
1.4 Categories of inductive systems.................... 53
1.5 Dissecting bornological vector spaces ................ 59
1.6 Metrisability and the approximation property ............ 67
2 Relations between entire, analytic, and local cyclic homology 74
2.1 Several definitions........................... 76
2.2 Comparison of analytic and local cyclic homology.......... 82
2.3 The local homotopy category of chain complexes.......... 84
2.4 Some counterexamples with compact Lie groups .......... 98
3 The spectral radius of bounded subsets and its applications 105
3.1 The spectral radius .......................... 106
3.2 Locally multiplicative bornological algebras............. 108
3.3 Analytically nilpotent bornological algebras............. 116
3.4 Isoradial homomorphisms....................... 117
3.5 Examples of isoradial homomorphisms................ 122
3.6 Isoradial hulls of subalgebras..................... 131
3.7 Passage to inductive systems..................... 135
4 Periodic cyclic homology via pro-nilpotent extensions 143
4.1 Pro-algebras.............................. 145
4.2 Homotopy invariance of periodic cyclic homology.......... 155
4.3 Excision in periodic cyclic homology................. 159
4.4 Exterior products........................... 173
5 Analytic cyclic homology and analytically nilpotent extensions 179
5.1 Lanilcurs and the analytic tensor algebra............... 180
5.2 Analytic cyclic homology via analytic tensor algebras........ 193
5.3 Basic properties............................ 197
5.4 Excision in analytic and local cyclic homology ........... 212
viii Contents
6 Local homotopy invariance and isoradial subalgebras 240
6.1 Local homotopy equivalences..................... 241
6.2 Approximate local homotopy equivalences.............. 247
6.3 Application to isoradial homomorphisms............... 250
6.4 Local and approximate local homotopy category........... 255
7 The Chern-Connes character 259
7.1 The Invariant Chern-Connes character................ 260
7.2 The Universal Coefficient Theorem.................. 266
7.3 The character for idempotents and invertibles............ 270
7.4 Finitely summable Fredholm modules................ 273
7.5 The character for general Fredholm modules............. 279
Appendix. Algebraic preliminaries 291
A.I Chain complexes over additive categories .............. 291
A.2 Basic constructions with algebras and modules............ 298
A.3 Non-commutative differential forms................. 308
A.4 Fedosov type products ........................ 314
A.5 Homological algebra for modules................... 321
A.6 Hochschild homology and cyclic homology............. 328
A.7 Biprojective algebras......................... 338
Bibliography 343
Notation and Symbols 349
Index 355
|
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| id | DE-604.BV025524297 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:35:56Z |
| institution | BVB |
| isbn | 9783037190395 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020132117 |
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| owner_facet | DE-11 DE-20 DE-355 DE-BY-UBR DE-83 |
| physical | VIII, 360 S. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | European Math. Soc. |
| record_format | marc |
| series | EMS tracts in mathematics |
| series2 | EMS tracts in mathematics |
| spelling | Meyer, Ralf 1974- Verfasser (DE-588)121506258 aut Local and analytic cyclic homology Ralf Meyer Zürich European Math. Soc. 2007 VIII, 360 S. txt rdacontent n rdamedia nc rdacarrier EMS tracts in mathematics 3 Banach-Algebra (DE-588)4193187-7 gnd rswk-swf K-Theorie (DE-588)4033335-8 gnd rswk-swf Bornologie (DE-588)4146354-7 gnd rswk-swf Zyklische Homologie (DE-588)4269326-3 gnd rswk-swf Zyklische Homologie (DE-588)4269326-3 s Bornologie (DE-588)4146354-7 s Banach-Algebra (DE-588)4193187-7 s K-Theorie (DE-588)4033335-8 s DE-604 EMS tracts in mathematics 3 (DE-604)BV022480257 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020132117&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Meyer, Ralf 1974- Local and analytic cyclic homology EMS tracts in mathematics Banach-Algebra (DE-588)4193187-7 gnd K-Theorie (DE-588)4033335-8 gnd Bornologie (DE-588)4146354-7 gnd Zyklische Homologie (DE-588)4269326-3 gnd |
| subject_GND | (DE-588)4193187-7 (DE-588)4033335-8 (DE-588)4146354-7 (DE-588)4269326-3 |
| title | Local and analytic cyclic homology |
| title_auth | Local and analytic cyclic homology |
| title_exact_search | Local and analytic cyclic homology |
| title_full | Local and analytic cyclic homology Ralf Meyer |
| title_fullStr | Local and analytic cyclic homology Ralf Meyer |
| title_full_unstemmed | Local and analytic cyclic homology Ralf Meyer |
| title_short | Local and analytic cyclic homology |
| title_sort | local and analytic cyclic homology |
| topic | Banach-Algebra (DE-588)4193187-7 gnd K-Theorie (DE-588)4033335-8 gnd Bornologie (DE-588)4146354-7 gnd Zyklische Homologie (DE-588)4269326-3 gnd |
| topic_facet | Banach-Algebra K-Theorie Bornologie Zyklische Homologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020132117&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022480257 |
| work_keys_str_mv | AT meyerralf localandanalyticcyclichomology |