Infinite homotopy theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
2001
|
| Series: | K-monographs in mathematics
6 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 296 S. zahlr. Ill. |
| ISBN: | 0792369823 |
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MARC
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| 245 | 1 | 0 | |a Infinite homotopy theory |c by Hans-Joachim Baues and Antonio Quintero |
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
Introduction 1
Chapter I. Foundations of homotopy theory and proper
homotopy theory 7
§ 1 Compactifications and compact maps 8
§ 2 Homotopy 18
§ 3 Categories with a cylinder functor 22
§ 4 Cofibration categories and homotopy theory in / categories 29
§ 5 Tracks and cylindrical homotopy groups 36
§ 6 Homotopy groups 44
§7Cofibres 50
Appendices 53
§ 8 Appendix. Compact maps 53
§ 9 Appendix. The Freudenthal compactification 57
Chapter II. Trees and spherical objects in the category
Topp of compact maps 71
§ 1 Locally finite trees and Freudenthal ends 71
Appendix. Halin s tree lemma 78
§ 2 Unions in Topp 80
Appendix. The proper Hilton Milnor theorem 87
§ 3 Spherical objects and homotopy groups in Topp 89
§4 The homotopy category of n dimensional spherical objects in
Topp 96
Appendix. Classification of spherical objects under a tree 103
Chapter III. Tree like spaces and spherical objects in the
category End of ended spaces 107
§ 1 Tree like spaces in End 107
§ 2 Unions in End 109
§3 Spherical objects and homotopy groups in End 113
§ 4 The homotopy category of n dimensional spherical objects in
End 117
Appendix. Classification of spherical objects under a tree like
space 122
§ 5 Z sets and telescopes 124
§ 6 ARZ spaces 130
Chapter IV. CW complexes 135
vi TABLE OF CONTENTS
§ 1 Relative CW complexes in Top 135
§ 2 Strongly locally finite CW complexes 140
§ 3 Relative CW complexes in Topp 142
§ 4 Relative CW complexes in End 148
§ 5 Normalization of CW complexes 154
§ 6 Push outs of CW complexes 157
§ 7 The Blakers Massey theorem 159
§ 8 The proper Whitehead theorem 163
Chapter V. Theories and models of theories 165
§ 1 Theories of cogroups and Van Kampen theorem for proper fun¬
damental groups 165
§ 2 Additive categories and additivization 175
§3 Rings associated to tree like spaces 185
§ 4 Inverse limits of gr(T) models 192
§5 Kernels in ab(T) 199
Chapter VI. T controlled homology 203
§ 1 R modules and the reduced projective class group 203
§ 2 Chain complexes in ringoids and homology 208
§ 3 Cellular T controlled homology 211
§ 4 Coefficients for T controlled homology and cohomology 215
§ 5 The Hurewicz theorem in End 221
§ 6 The proper homological Whitehead theorem (the 1 connected
case) 224
§ 7 Proper finiteness obstructions (the 1 connected case) 225
Chapter VII. Proper groupoids 229
§ 1 Filtered discrete objects 229
§ 2 The fundamental groupoid of ended spaces 232
§ 3 The proper homotopy category of 1 dimensional reduced relative
CW complexes 236
§ 4 Free X groupoids under G 237
§ 5 The proper fundamental groupoid of a 1 dimensional reduced
relative CW complex 242
§ 6 Simplicial objects in proper homotopy theory 244
Chapter VIII. The enveloping ringoid of a proper grou¬
poid 249
§ 1 The homotopy category of 1 dimensional spherical objects under
T 249
§ 2 The ringoid S(X, T) associated to a pair (X, T) in End 250
§ 3 The enveloping ringoid of the proper fundamental group 253
§ 4 The enveloping ringoid of the proper fundamental groupoid 256
Chapter IX. T controlled homology with coefficients 261
§ 1 The T controlled twisted chain complex of a relative CW complex
(X,T) 261
§ 2 The T controlled twisted chain complex of a CW complex X 266
INFINITE HOMOTOPY THEORY vii
§ 3 T controlled cohomology and homology with local coefficients 268
§ 4 Proper obstruction theory 269
§ 5 The twisted Hurewicz homomorphism and the twisted F sequence
in ooEnd 270
§ 6 The proper homological Whitehead theorem (the 0 connected
case) 273
§ 7 Proper finiteness obstructions (the 0 connected case) 274
Chapter X. Simple homotopy types with ends 275
§ 1 The torsion group Kx 275
§ 2 Simple equivalences and proper equivalences 277
§ 3 The topological Whitehead group 279
§ 4 The algebraic Whitehead group 280
§ 5 The proper algebraic Whitehead group 282
Bibliography 285
Subject Index 291
List of symbols 295
|
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| author | Baues, Hans J. 1943- Quintero, Antonio |
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| id | DE-604.BV014262216 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:00:37Z |
| institution | BVB |
| isbn | 0792369823 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009781233 |
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| physical | VII, 296 S. zahlr. Ill. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
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| publisher | Kluwer |
| record_format | marc |
| series | K-monographs in mathematics |
| series2 | K-monographs in mathematics |
| spelling | Baues, Hans J. 1943- Verfasser (DE-588)128430702 aut Infinite homotopy theory by Hans-Joachim Baues and Antonio Quintero Dordrecht [u.a.] Kluwer 2001 VII, 296 S. zahlr. Ill. txt rdacontent n rdamedia nc rdacarrier K-monographs in mathematics 6 Homotopie Homotopy theory Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 s DE-604 Quintero, Antonio Verfasser aut K-monographs in mathematics 6 (DE-604)BV011222840 6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009781233&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baues, Hans J. 1943- Quintero, Antonio Infinite homotopy theory K-monographs in mathematics Homotopie Homotopy theory Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (DE-588)4128142-1 |
| title | Infinite homotopy theory |
| title_auth | Infinite homotopy theory |
| title_exact_search | Infinite homotopy theory |
| title_full | Infinite homotopy theory by Hans-Joachim Baues and Antonio Quintero |
| title_fullStr | Infinite homotopy theory by Hans-Joachim Baues and Antonio Quintero |
| title_full_unstemmed | Infinite homotopy theory by Hans-Joachim Baues and Antonio Quintero |
| title_short | Infinite homotopy theory |
| title_sort | infinite homotopy theory |
| topic | Homotopie Homotopy theory Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Homotopie Homotopy theory Homotopietheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009781233&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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