Ends of complexes:
The ends of a topological space are the directions in which it becomes non-compact by tending to infinity. The tame ends of manifolds are particularly interesting, both for their own sake, and for their use in the classification of high-dimensional compact manifolds. This book is devoted to the rela...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
1996
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge tracts in mathematics
123 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | The ends of a topological space are the directions in which it becomes non-compact by tending to infinity. The tame ends of manifolds are particularly interesting, both for their own sake, and for their use in the classification of high-dimensional compact manifolds. This book is devoted to the related theory and practice of ends, dealing with manifolds and CW complexes in topology and chain complexes in algebra. The first part develops a homotopy model of the behaviour of infinity of a non-compact space. The second part studies tame ends in topology. Tame ends are shown to have a uniform structure, with a periodic shift map. Approximate fibrations are used to prove that tame manifold ends are the infinite cyclic covers of compact manifolds. The third part translates these topological considerations into an appropriate algebraic context, relating tameness to homological properties and algebraic K- and L-theory. |
| Beschreibung: | XXV, 353 S. graph. Darst. |
| ISBN: | 0521576253 |
Internformat
MARC
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| 490 | 1 | |a Cambridge tracts in mathematics |v 123 | |
| 520 | 3 | |a The ends of a topological space are the directions in which it becomes non-compact by tending to infinity. The tame ends of manifolds are particularly interesting, both for their own sake, and for their use in the classification of high-dimensional compact manifolds. This book is devoted to the related theory and practice of ends, dealing with manifolds and CW complexes in topology and chain complexes in algebra. The first part develops a homotopy model of the behaviour of infinity of a non-compact space. The second part studies tame ends in topology. Tame ends are shown to have a uniform structure, with a periodic shift map. Approximate fibrations are used to prove that tame manifold ends are the infinite cyclic covers of compact manifolds. The third part translates these topological considerations into an appropriate algebraic context, relating tameness to homological properties and algebraic K- and L-theory. | |
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Datensatz im Suchindex
| _version_ | 1804125563396292608 |
|---|---|
| adam_text | Contents
Introduction page ix
Chapter summaries xxii
Part one Topology at infinity 1
1 End spaces 1
2 Limits 13
3 Hoinology at infinity 29
4 Cellular homology 43
5 Homology of covers 56
6 Projective class and torsion 65
7 Forward tameness 75
8 Reverse tameness 92
9 Homotopy at infinity 97
10 Projective class at infinity 109
11 Infinite torsion 122
12 Forward tameness is a homotopy pushout 137
Part two Topology over the real line 147
13 Infinite cyclic covers 147
14 The mapping torus 168
15 Geometric ribbons and bands 173
16 Approximate fibrations 187
17 Geometric wrapping up 197
18 Geometric relaxation 214
19 Homotopy theoretic twist glueing 222
20 Homotopy theoretic wrapping up and relaxation 244
Part three The algebraic theory 255
21 Polynomial extensions 255
22 Algebraic bands 263
23 Algebraic tameness 268
24 Relaxation techniques 288
25 Algebraic ribbons 300
26 Algebraic twist glueing 306
27 Wrapping up in algebraic K and L theory 318
vii
viii Ends of complexes
Part four Appendices 325
Appendix A. Locally finite homology with local coefficients 325
Appendix B. A brief history of end spaces 335
Appendix C. A brief history of wrapping up 338
References 341
Index 351
|
| any_adam_object | 1 |
| author | Hughes, Bruce Ranicki, Andrew 1948-2018 |
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| bvnumber | BV011073006 |
| callnumber-first | Q - Science |
| callnumber-label | QA608 |
| callnumber-raw | QA608 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 300 SK 350 |
| ctrlnum | (OCoLC)34517006 (DE-599)BVBBV011073006 |
| dewey-full | 514/.223 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.223 |
| dewey-search | 514/.223 |
| dewey-sort | 3514 3223 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV011073006 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:03:33Z |
| institution | BVB |
| isbn | 0521576253 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007417273 |
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| physical | XXV, 353 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Hughes, Bruce Verfasser aut Ends of complexes Bruce Hughes ; Andrew Ranicki 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1996 XXV, 353 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 123 The ends of a topological space are the directions in which it becomes non-compact by tending to infinity. The tame ends of manifolds are particularly interesting, both for their own sake, and for their use in the classification of high-dimensional compact manifolds. This book is devoted to the related theory and practice of ends, dealing with manifolds and CW complexes in topology and chain complexes in algebra. The first part develops a homotopy model of the behaviour of infinity of a non-compact space. The second part studies tame ends in topology. Tame ends are shown to have a uniform structure, with a periodic shift map. Approximate fibrations are used to prove that tame manifold ends are the infinite cyclic covers of compact manifolds. The third part translates these topological considerations into an appropriate algebraic context, relating tameness to homological properties and algebraic K- and L-theory. Topologische ruimten gtt Uitbreidingen gtt Complexes CW-Komplex (DE-588)4148419-8 gnd rswk-swf Komplex Algebra (DE-588)4164880-8 gnd rswk-swf CW-Komplex (DE-588)4148419-8 s DE-604 Komplex Algebra (DE-588)4164880-8 s Ranicki, Andrew 1948-2018 Verfasser (DE-588)120140500 aut Cambridge tracts in mathematics 123 (DE-604)BV000000001 123 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007417273&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hughes, Bruce Ranicki, Andrew 1948-2018 Ends of complexes Cambridge tracts in mathematics Topologische ruimten gtt Uitbreidingen gtt Complexes CW-Komplex (DE-588)4148419-8 gnd Komplex Algebra (DE-588)4164880-8 gnd |
| subject_GND | (DE-588)4148419-8 (DE-588)4164880-8 |
| title | Ends of complexes |
| title_auth | Ends of complexes |
| title_exact_search | Ends of complexes |
| title_full | Ends of complexes Bruce Hughes ; Andrew Ranicki |
| title_fullStr | Ends of complexes Bruce Hughes ; Andrew Ranicki |
| title_full_unstemmed | Ends of complexes Bruce Hughes ; Andrew Ranicki |
| title_short | Ends of complexes |
| title_sort | ends of complexes |
| topic | Topologische ruimten gtt Uitbreidingen gtt Complexes CW-Komplex (DE-588)4148419-8 gnd Komplex Algebra (DE-588)4164880-8 gnd |
| topic_facet | Topologische ruimten Uitbreidingen Complexes CW-Komplex Komplex Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007417273&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000001 |
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