Classical topology and combinatorial group theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1993
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Graduate texts in mathematics
72 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Literaturverz. S. [307] - 318 |
| Beschreibung: | XII, 334 S. Ill., graph. Darst. |
| ISBN: | 0387979700 3540979700 |
Internformat
MARC
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| 245 | 1 | 0 | |a Classical topology and combinatorial group theory |c John Stillwell |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1993 | |
| 300 | |a XII, 334 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Graduate texts in mathematics |v 72 | |
| 500 | |a Literaturverz. S. [307] - 318 | ||
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Datensatz im Suchindex
| _version_ | 1804121400313643008 |
|---|---|
| adam_text | This is a well-balanced introduction to topology that stresses geometric
aspects. Focusing on historical background and visual interpretation of
results, it emphasizes spaces with few dimensions, where visualization
is possible, and interaction with combinatorial group theory via the
fundamental group. It also presents algorithms for topological prob¬
lems. Most of the results and proofs are known, but some have been
simplified or placed in a new perspective.
Over
300
illustrations, many interesting exercises, and challenging
open problems are included. New in this edition is a chapter on unsolv-
able problems, which includes the first textbook proof that the main
problem of topology, the homeomorphism problem, is unsolvable.
Contents
Preface
to the First Edition
vii
Preface to the Second Edition
ix
CHAPTER
0
Introduction and Foundations
1
0.1
The Fundamental Concepts and Problems of Topology
2
0.2
Simplicial Complexes
19
0.3
The Jordan Curve Theorem
26
0.4
Algorithms
36
0.5
Combinatorial Group Theory
40
CHAPTER I
Complex Analysis and Surface Topology
53
1.1
Riemann Surfaces
54
Î
.2
Nonorientable Surfaces
62
1.3
The Classification Theorem for Surfaces
69
J
.4
Covering Surfaces
80
CHAPTER
2
Graphs and Free Groups
89
2.
ł
Realization of Free Groups by Graphs
90
2.2
Realization of Subgroups
99
CHAPTER
3
Foundations for the Fundamental Group
109
3.1
The Fundamental Group
110
3.2
The Fundamental Group of the Circle
116
3.3
Deformation Retracts
121
3.4
The
Seifert-
Van
Kampen
Theorem
124
3.5
Direct Products
132
Contents
CHAPTER
4
Fundamental Groups of Complexes
135
4.1
Poincaré s
Method for Computing Presentations
136
4.2
Examples
141
4.3
Surface Complexes and Subgroup Theorems
156
CHAPTER
5
Homology Theory and Abelianization
169
5.1
Homology Theory
170
5.2
The Structure Theorem for Finitely Generated Abelian Groups
175
5.3
Abelianization
181
CHAPTER
6
Curves on Surfaces
185
6.1
Dehn s Algorithm
186
6.2
Simple Curves on Surfaces
190
6.3
Simplification of Simple Curves by Homeomorphisms
196
6.4
The Mapping Class Group of the Torus
206
CHAPTER
7
Knots and Braids
217
7.1 Dehn
and Schreier s Analysis of the Torus Knot Groups
218
7.2
Cyclic Coverings
225
7.3
Braids
233
CHAPTER
8
Three-Dimensional Manifolds
241
8.1
Open Problems in Three-Dimensional Topology
242
8.2
Polyhedral Schemata
248
8.3
Heegaard Splittings
252
8.4
Surgery
263
8.5
Branched Coverings
270
CHAPTER
9
Unsolvable Problems
275
9.1
Computation
276
9.2
HNN Extensions
285
9.3
Unsolvable Problems in Group Theory
290
9.4
The Homeomorphism
РтоЫет
298
Bibliography and Chronology
307
Index
319
|
| any_adam_object | 1 |
| author | Stillwell, John 1942- |
| author_GND | (DE-588)128427264 |
| author_facet | Stillwell, John 1942- |
| author_role | aut |
| author_sort | Stillwell, John 1942- |
| author_variant | j s js |
| building | Verbundindex |
| bvnumber | BV007193305 |
| classification_rvk | SK 260 SK 620 |
| classification_tum | MAT 550f MAT 200f |
| ctrlnum | (OCoLC)439527338 (DE-599)BVBBV007193305 |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV007193305 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:57:23Z |
| institution | BVB |
| isbn | 0387979700 3540979700 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004601310 |
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| physical | XII, 334 S. Ill., graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Stillwell, John 1942- Verfasser (DE-588)128427264 aut Classical topology and combinatorial group theory John Stillwell 2. ed. New York [u.a.] Springer 1993 XII, 334 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 72 Literaturverz. S. [307] - 318 Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Kombinatorische Topologie (DE-588)4137530-0 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Kombinatorische Gruppentheorie (DE-588)4219556-1 s Topologie (DE-588)4060425-1 s DE-604 Gruppentheorie (DE-588)4072157-7 s Kombinatorik (DE-588)4031824-2 s Kombinatorische Topologie (DE-588)4137530-0 s 2\p DE-604 Graduate texts in mathematics 72 (DE-604)BV000000067 72 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004601310&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004601310&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Stillwell, John 1942- Classical topology and combinatorial group theory Graduate texts in mathematics Gruppentheorie (DE-588)4072157-7 gnd Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd Kombinatorik (DE-588)4031824-2 gnd Topologie (DE-588)4060425-1 gnd Kombinatorische Topologie (DE-588)4137530-0 gnd |
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| title | Classical topology and combinatorial group theory |
| title_auth | Classical topology and combinatorial group theory |
| title_exact_search | Classical topology and combinatorial group theory |
| title_full | Classical topology and combinatorial group theory John Stillwell |
| title_fullStr | Classical topology and combinatorial group theory John Stillwell |
| title_full_unstemmed | Classical topology and combinatorial group theory John Stillwell |
| title_short | Classical topology and combinatorial group theory |
| title_sort | classical topology and combinatorial group theory |
| topic | Gruppentheorie (DE-588)4072157-7 gnd Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd Kombinatorik (DE-588)4031824-2 gnd Topologie (DE-588)4060425-1 gnd Kombinatorische Topologie (DE-588)4137530-0 gnd |
| topic_facet | Gruppentheorie Kombinatorische Gruppentheorie Kombinatorik Topologie Kombinatorische Topologie Lehrbuch |
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| volume_link | (DE-604)BV000000067 |
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