Combinatorial foundation of homology and homotopy: applications to spaces, diagrams, transformation groups, compactifications, differential algebras, algebraic theories, simplicial objects, and resolutions
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin ; Heidelberg ; New York ; Barcelona ; Budapest
Springer
1999
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| Series: | Springer monographs in mathematics
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| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008294186&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XV, 362 S. |
| ISBN: | 3540649840 |
Staff View
MARC
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| 245 | 1 | 0 | |a Combinatorial foundation of homology and homotopy |b applications to spaces, diagrams, transformation groups, compactifications, differential algebras, algebraic theories, simplicial objects, and resolutions |c Hans Joachim Baues |
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; Barcelona ; Budapest |b Springer |c 1999 | |
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| 490 | 0 | |a Springer monographs in mathematics | |
| 650 | 4 | |a Algebraische Topologie | |
| 650 | 4 | |a Homologietheorie | |
| 650 | 4 | |a Homotopietheorie | |
| 650 | 4 | |a Combinatorial analysis | |
| 650 | 4 | |a Homology theory | |
| 650 | 4 | |a Homotopy theory | |
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Record in the Search Index
| _version_ | 1819262105379930112 |
|---|---|
| adam_text | Table of Contents
Preface V
Leitfaden XI
Fields of Application XIII
Part I. Examples and Applications
Chapter A: Examples and Applications in Topological Categories .. 3
1 Homotopy Theory of Spaces Under a Space 3
2 Homotopy Theory of Diagrams of Spaces 18
3 Homotopy Theory of Transformation Groups 31
4 Homotopy Theory Controlled at Infinity 40
Chapter B: Examples and Applications
in Algebraic Homotopy Theories 51
1 Homotopy Theory of Chain Algebras 51
2 Homotopy Theory of Connected Simplicial Objects
in Algebraic Theories 61
Chapter C: Applications and Examples
in Delicate Homotopy Theories of Simplicial Objects 71
1 Homotopy Theory of Free Simplicial Objects
in Theories of Coactions 71
2 Examples of Theories of Coactions Satisfying
the Delicate Blakers Massey Property 87
3 Polynomial Theories of Cogroups 89
4 Algebras over an Operad 95
Chapter D: Resolutions in Model Categories 99
1 Quillen Model Categories 99
2 Spiral Model Categories 101
3 Spiral Homotopy Theory 110
4 Spiral Homotopy Groups 115
VIII Table of Contents
5 Examples of Spiral Model Categories 118
6 Homology and Cohomology in Spiral Homotopy Theory 120
7 Spiral Resolutions and Spiral Realizations 124
Part II. Combinatorial Homology and Homotopy
Chapter I: Theories of Coactions and Homology 129
1 Theories of Cogroups and Theories of Coactions 129
2 Examples 134
3 The Category of Twisted Maps 139
4 The Category of Coefficients 145
5 Enveloping Functors and the Categories
of Premodules and Modules 149
6 Chain Complexes and Homology 156
7 Augmented Theories of Coactions 161
Chapter II: Twisted Chain Complexes and Twisted Homology 169
1 Twisted Chain Complexes 170
2 The Module Fj 174
3 The Obstruction for the Twisted Realization of a Chain Map 177
4 Twisted Homotopies 182
5 Twisted Homotopy Equivalences 187
6 The Augmentation Functor 192
7 Appendix: Homology of Coefficient Objects 193
8 Appendix: Twisted Homology of Coefficient Objects 197
Chapter III: Basic Concepts of Homotopy Theory 203
1 Cofibration Categories 203
2 Homotopy Groups 207
3 Principal Cofibrations 209
4 The Cylinder of Pairs 214
5 Homotopy Cogroups and Homotopy Coactions 215
6 The Theories susp(*) and cone(*) 217
7 Appendix: Categories with a Cylinder Functor 221
8 Appendix: Natural Cylinder Categories
and Homotopy Theory of Diagrams 223
9 Appendix: Homotopy Theory of Chain Complexes 225
Chapter IV: Complexes in Cofibration Categories 229
1 Filtered Objects 229
2 Complexes Associated to Theories of Coactions 231
3 The Whitehead Theorem 234
4 Cellular Approximation 240
5 The Blakers Massey Property 245
Table of Contents IX
Chapter V: Homology of Complexes 249
1 Homological Cofibration Categories 249
2 The Chains of a Complex 254
3 The Homology of a Complex 257
4 The Obstruction Cocycle 260
5 The Hurewicz Homomorphism and Whitehead s Exact Sequence. . . 262
Chapter V: Homology of Complexes 267
1 Twisted Homotopy Systems of Order n 267
2 Obstructions for the Realizability of Chain Maps 271
3 The Homotopy Lifting Property of the Chain Functor 276
4 Counting Realization of Chain Maps 277
5 Linear Extensions and Towers of Categories 279
6 The Homological Tower of Categories 283
7 The Homological Whitehead Theorem 286
8 The Model Lifting Property of the Twisted Chain Functor 287
9 Obstructions for the Realizability of Twisted Chain Complexes .... 291
10 The Hurewicz Theorem 294
11 Appendix: Eilenberg Mac Lane Complexes and (C, T) Homology
of Coefficient Objects 296
Chapter VII: Finiteness Obstructions 301
1 The Reduced Projective Class Group 301
2 The Finiteness Obstruction Theorem 303
3 Finiteness Obstructions for Twisted Chain Complexes 304
4 Proof of the Finiteness Obstruction Theorem 312
Chapter VIII: Non Reduced Complexes and Whitehead Torsion . . . 315
1 Classes of Discrete Objects 315
2 Cells in a Cofibration Category 317
3 Non Reduced Complexes 319
4 The Ball Pair Axiom 323
5 Cellular / Categories 327
6 Elementary Expansions 328
7 Formal Deformations and Simple Homotopy Equivalences 330
8 The Whitehead Group and Whitehead Torsion 334
9 Simplified Form of Elements in the Whitehead Group 339
10 The Torsion Group Kl 342
11 The Algebraic Whitehead Group 344
12 The Isomorphism Between the Geometric
and Algebraic Whitehead Group 345
Index 355
List of Notations 361
|
| any_adam_object | 1 |
| author | Baues, Hans J. 1943- |
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| dewey-full | 514.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.23 |
| dewey-search | 514.23 |
| dewey-sort | 3514.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012240124 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:26:50Z |
| institution | BVB |
| isbn | 3540649840 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008294186 |
| oclc_num | 246123075 |
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| physical | XV, 362 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer monographs in mathematics |
| spellingShingle | Baues, Hans J. 1943- Combinatorial foundation of homology and homotopy applications to spaces, diagrams, transformation groups, compactifications, differential algebras, algebraic theories, simplicial objects, and resolutions Algebraische Topologie Homologietheorie Homotopietheorie Combinatorial analysis Homology theory Homotopy theory Algebraische Topologie (DE-588)4120861-4 gnd Homologietheorie (DE-588)4141714-8 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (DE-588)4120861-4 (DE-588)4141714-8 (DE-588)4128142-1 |
| title | Combinatorial foundation of homology and homotopy applications to spaces, diagrams, transformation groups, compactifications, differential algebras, algebraic theories, simplicial objects, and resolutions |
| title_auth | Combinatorial foundation of homology and homotopy applications to spaces, diagrams, transformation groups, compactifications, differential algebras, algebraic theories, simplicial objects, and resolutions |
| title_exact_search | Combinatorial foundation of homology and homotopy applications to spaces, diagrams, transformation groups, compactifications, differential algebras, algebraic theories, simplicial objects, and resolutions |
| title_full | Combinatorial foundation of homology and homotopy applications to spaces, diagrams, transformation groups, compactifications, differential algebras, algebraic theories, simplicial objects, and resolutions Hans Joachim Baues |
| title_fullStr | Combinatorial foundation of homology and homotopy applications to spaces, diagrams, transformation groups, compactifications, differential algebras, algebraic theories, simplicial objects, and resolutions Hans Joachim Baues |
| title_full_unstemmed | Combinatorial foundation of homology and homotopy applications to spaces, diagrams, transformation groups, compactifications, differential algebras, algebraic theories, simplicial objects, and resolutions Hans Joachim Baues |
| title_short | Combinatorial foundation of homology and homotopy |
| title_sort | combinatorial foundation of homology and homotopy applications to spaces diagrams transformation groups compactifications differential algebras algebraic theories simplicial objects and resolutions |
| title_sub | applications to spaces, diagrams, transformation groups, compactifications, differential algebras, algebraic theories, simplicial objects, and resolutions |
| topic | Algebraische Topologie Homologietheorie Homotopietheorie Combinatorial analysis Homology theory Homotopy theory Algebraische Topologie (DE-588)4120861-4 gnd Homologietheorie (DE-588)4141714-8 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Algebraische Topologie Homologietheorie Homotopietheorie Combinatorial analysis Homology theory Homotopy theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008294186&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT baueshansj combinatorialfoundationofhomologyandhomotopyapplicationstospacesdiagramstransformationgroupscompactificationsdifferentialalgebrasalgebraictheoriessimplicialobjectsandresolutions |