The Lefschetz fixed point theorem:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Glenview, Ill.
Scott, Foresman
1971
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 186 S. graph. Darst. |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804116387838296064 |
|---|---|
| adam_text | Contents
I. PRELIMINARIES 1
A. Graded Modules 1
B. Traces 2
C. Chain Complexes and Cohomology 3
D. The Hopf Trace Theorem 5
E. Simplicial Complexes 8
F. Barycentric Subdivision 9
G. The Euler Characteristic 9
H. Geometric Realization 10
I. Simplicial Approximation 12
J. Singular Cohomology Theory 13
K. The Cup Product 14
L. The Identification Theorem 15
M. Relative Singular Cohomology 16
N. The Fundamental Group 22
Notes 24
Exercises 24
II. THE LEFSCHETZ THEOREM FOR POLYHEDRA 25
A. The Lefschetz Theorem 25
B. The Figure Eight 28
C. The Fixed Point Property 30
D. Deformations 32
Notes 33
Exercises 34
III. THE LEFSCHETZ THEOREM FOR ANRs 37
A. Absolute Neighborhood Retracts 37
B. The Domination Theorem 40
CONTENTS V
C. The Lefschetz Theorem 42
D. Q Acyclic Spaces 43
E. Fixed Points of Homeomorphisms 44
F. Topological Groups 47
Notes 49
Exercises 50
IV. INDEX THEORY FOR POLYHEDRA 51
A. The Axioms for an Index 52
B. The Index 54
C. The Lefschetz Number 65
D. The Normalization Axiom 67
E. The Figure Eight Again 72
Notes 73
Exercises 74
V. INDEX THEORY FOR ANRs 75
A. The Index for ANRs 75
B. Proof of the Invariance Theorem 77
C. Verification of the Axioms 80
Notes 84
Exercises 84
VI. THE NIELSEN NUMBER 85
A. Paths 85
B. Fixed Point Classes 86
C. The Nielsen Number 87
D. // Related Classes 87
E. Invariance Under Homotopy 92
Notes 96
Exercises 96
vi CONTENTS
VII. COMPUTATION OF THE NIELSEN NUMBER 97
A. The Jiang Subgroup 97
B. Bounds on the Nielsen Number 103
C. Examples 106
D. The Number of fcth Roots 109
E. A Final Look at the Figure Eight 111
Notes 113
Exercises 113
VIII. THE CONVERSE OF THE LEFSCHETZ THEOREM 115
A. Finite Fixed Point Sets 115
B. Points of Index Zero 119
C. Points in the Same Class 124
D. The Converse of the Lefschetz Theorem 139
E. Deformations 142
F. The Fixed Point Property 146
Notes 150
Exercises 151
APPENDIX I. DOLD S LEMMA 153
APPENDIX II. UNIQUENESS OF THE INDEX 165
A. Uniqueness on Geometric Complexes 165
B. Uniqueness on ANRs 172
Notes 173
BIBLIOGRAPHY 175
INDEX 178
|
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| ctrlnum | (OCoLC)318168555 (DE-599)BVBBV001946780 |
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| dewey-ones | 514 - Topology |
| dewey-raw | 514.322 |
| dewey-search | 514.322 |
| dewey-sort | 3514.322 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV001946780 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:37:42Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001269024 |
| oclc_num | 318168555 |
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| physical | VI, 186 S. graph. Darst. |
| publishDate | 1971 |
| publishDateSearch | 1971 |
| publishDateSort | 1971 |
| publisher | Scott, Foresman |
| record_format | marc |
| spelling | Brown, Robert F. Verfasser aut The Lefschetz fixed point theorem Robert F. Brown Glenview, Ill. Scott, Foresman 1971 VI, 186 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Teoría del punto fijo Lefschetz-Fixpunktsatz (DE-588)4501113-8 gnd rswk-swf Lefschetz-Fixpunktsatz (DE-588)4501113-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001269024&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brown, Robert F. The Lefschetz fixed point theorem Teoría del punto fijo Lefschetz-Fixpunktsatz (DE-588)4501113-8 gnd |
| subject_GND | (DE-588)4501113-8 |
| title | The Lefschetz fixed point theorem |
| title_auth | The Lefschetz fixed point theorem |
| title_exact_search | The Lefschetz fixed point theorem |
| title_full | The Lefschetz fixed point theorem Robert F. Brown |
| title_fullStr | The Lefschetz fixed point theorem Robert F. Brown |
| title_full_unstemmed | The Lefschetz fixed point theorem Robert F. Brown |
| title_short | The Lefschetz fixed point theorem |
| title_sort | the lefschetz fixed point theorem |
| topic | Teoría del punto fijo Lefschetz-Fixpunktsatz (DE-588)4501113-8 gnd |
| topic_facet | Teoría del punto fijo Lefschetz-Fixpunktsatz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001269024&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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