Introduction to topological manifolds:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
[2011]
|
| Ausgabe: | Second edition |
| Schriftenreihe: | Graduate texts in mathematics
202 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xvii, 433 Seiten Illustrationen, Diagramme |
| ISBN: | 9781441979391 9781461427902 |
Internformat
MARC
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|---|---|---|---|
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| 003 | DE-604 | ||
| 005 | 20220330 | ||
| 007 | t | ||
| 008 | 110217s2011 gw a||| |||| 00||| eng d | ||
| 020 | |a 9781441979391 |c hardcover |9 978-1-4419-7939-1 | ||
| 020 | |a 9781461427902 |c softcover |9 978-1-4614-2790-2 | ||
| 035 | |a (OCoLC)700650008 | ||
| 035 | |a (DE-599)BVBBV037232325 | ||
| 040 | |a DE-604 |b ger |e rda | ||
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| 100 | 1 | |a Lee, John M. |d 1950- |e Verfasser |0 (DE-588)122260880 |4 aut | |
| 245 | 1 | 0 | |a Introduction to topological manifolds |c John M. Lee |
| 250 | |a Second edition | ||
| 264 | 1 | |a New York, NY |b Springer |c [2011] | |
| 264 | 4 | |c © 2011 | |
| 300 | |a xvii, 433 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 202 | |
| 650 | 0 | 7 | |a Topologische Mannigfaltigkeit |0 (DE-588)4185712-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Topologische Mannigfaltigkeit |0 (DE-588)4185712-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4419-7940-7 |
| 830 | 0 | |a Graduate texts in mathematics |v 202 |w (DE-604)BV000000067 |9 202 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021145981&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-021145981 | ||
Datensatz im Suchindex
| _version_ | 1804143838871158784 |
|---|---|
| adam_text | Contents
Preface
............................................................
v
1
Introduction
................................................... 1
What Are Manifolds?
............................................ 1
Why Study Manifolds?
........................................... 4
2
Topological Spaces
............................................. 19
Topologies
..................................................... 19
Convergence and Continuity
...................................... 26
Hausdorff Spaces
............................................... 31
Bases and Countability
........................................... 33
Manifolds
...................................................... 38
Problems
...................................................... 45
3
New Spaces from Old
........................................... 49
Subspaces
..................................................... 49
Product Spaces
................................................. 60
Disjoint Union Spaces
........................................... 64
Quotient Spaces
................................................ 65
Adjunction Spaces
.............................................. 73
Topological Groups and Group Actions
............................. 77
Problems
...................................................... 81
4
Connectedness and Compactness
................................ 85
Connectedness
.................................................. 86
Compactness
................................................... 94
Local Compactness
.............................................. 104
Paracompactness
................................................ 109
Proper Maps
...................................................
1 8
Problems
...................................................... 122
xvj Contents
5
Cell Complexes
................................................127
Cell Complexes and CW Complexes
...............................127
Topological Properties of CW Complexes
...........................135
Classification of
1
-Dimensional Manifolds
..........................143
Simplicial Complexes
............................................147
Problems
......................................................155
6
Compact Surfaces
..............................................159
Surfaces
.......................................................159
Connected Sums of Surfaces
......................................164
Polygonal Presentations of Surfaces
................................166
The Classification Theorem
.......................................173
The
Euler
Characteristic
..........................................178
Orientability
...................................................180
Problems
......................................................181
7
Homotopy and the Fundamental Group
..........................183
Homotopy
.....................................................184
The Fundamental Group
.........................................186
Homomorphisms Induced by Continuous Maps
......................197
Homotopy Equivalence
..........................................200
Higher Homotopy Groups
........................................208
Categories and Functors
..........................................209
Problems
......................................................214
8
The Circle
.....................................................217
Lifting Properties of the Circle
....................................218
The Fundamental Group of the Circle
..............................224
Degree Theory for the Circle
......................................227
Problems
......................................................230
9
Some Group Theory
............................................233
Free Products
...................................................233
Free Groups
....................................................239
Presentations of Groups
..........................................241
Free Abelian Groups
.............................................244
Problems
......................................................248
10
The Seifert-Van
Kampen
Theorem
...............................251
Statement of the Theorem
........................................251
Applications
...................................................255
Fundamental Groups of Compact Surfaces
..........................264
Proof of the Seifert-Van
Kampen
Theorem
..........................268
Problems
......................................................273
Contents xvii
11
Covering Maps
................................................277
Definitions and Basic Properties
...................................278
The General Lifting Problem
......................................283
The Monodromy Action
..........................................287
Covering Homomorphisms
.......................................294
The Universal Covering Space
....................................297
Problems
......................................................302
12
Group Actions and Covering Maps
...............................307
The Automorphism Group of a Covering
............................308
Quotients by Group Actions
......................................311
The Classification Theorem
.......................................315
Proper Group Actions
............................................318
Problems
......................................................334
13
Homology
.....................................................339
Singular Homology Groups
.......................................340
Homotopy
Invariance
............................................347
Homology and the Fundamental Group
.............................351
The Mayer-Vietoris Theorem
.....................................355
Homology of Spheres
............................................364
Homology of CW Complexes
.....................................369
Cohomology
...................................................374
Problems
......................................................379
Appendix A: Review of Set Theory
...................................381
Basic Concepts
.................................................381
Cartesian Products, Relations, and Functions
........................384
Number Systems and Cardinality
..................................390
Indexed Families
................................................391
Appendix B: Review of Metric Spaces
................................395
Euclidean Spaces
...............................................395
Metrics
........................................................396
Continuity and Convergence
......................................398
Appendix C: Review of Group Theory
................................401
Basic Definitions
................................................401
Cosets and Quotient Groups
......................................403
Cyclic Groups
..................................................405
References
.........................................................407
Notation Index
.....................................................409
Subject Index
......................................................413
|
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| id | DE-604.BV037232325 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:54:02Z |
| institution | BVB |
| isbn | 9781441979391 9781461427902 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021145981 |
| oclc_num | 700650008 |
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| physical | xvii, 433 Seiten Illustrationen, Diagramme |
| publishDate | 2011 |
| publishDateSearch | 2011 |
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| publisher | Springer |
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| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Lee, John M. 1950- Verfasser (DE-588)122260880 aut Introduction to topological manifolds John M. Lee Second edition New York, NY Springer [2011] © 2011 xvii, 433 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 202 Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd rswk-swf Topologische Mannigfaltigkeit (DE-588)4185712-4 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4419-7940-7 Graduate texts in mathematics 202 (DE-604)BV000000067 202 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021145981&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lee, John M. 1950- Introduction to topological manifolds Graduate texts in mathematics Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd |
| subject_GND | (DE-588)4185712-4 |
| title | Introduction to topological manifolds |
| title_auth | Introduction to topological manifolds |
| title_exact_search | Introduction to topological manifolds |
| title_full | Introduction to topological manifolds John M. Lee |
| title_fullStr | Introduction to topological manifolds John M. Lee |
| title_full_unstemmed | Introduction to topological manifolds John M. Lee |
| title_short | Introduction to topological manifolds |
| title_sort | introduction to topological manifolds |
| topic | Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd |
| topic_facet | Topologische Mannigfaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021145981&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
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