Introduction to topology:
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Book |
| Language: | English Russian |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2001]
|
| Series: | Student mathematical library
volume 14 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 149 Seiten Illustrationen, Diagramme |
| ISBN: | 0821821628 9780821821626 |
Staff View
MARC
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| 100 | 1 | |a Vasilʹev, Vjačeslav A. |e Verfasser |0 (DE-588)120817896 |4 aut | |
| 240 | 1 | 0 | |a Vvedenie v topologiju |
| 245 | 1 | 0 | |a Introduction to topology |c V. A. Vassiliev. Translated by A. Sossinski |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2001] | |
| 264 | 4 | |c © 2001 | |
| 300 | |a xiii, 149 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Student mathematical library |v volume 14 | |
| 650 | 7 | |a Algebraïsche topologie |2 gtt | |
| 650 | 4 | |a Topologie | |
| 650 | 4 | |a Topology | |
| 650 | 0 | 7 | |a Topologie |0 (DE-588)4060425-1 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Sossinsky, A. B. |d 1937- |0 (DE-588)122444817 |4 trl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-2130-4 |
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Record in the Search Index
| _version_ | 1804128713198010368 |
|---|---|
| adam_text | Contents
Foreword
xi
Chapter
1.
Topological spaces and operations with them
1
§1.1.
Topological spaces and homeomorphisms
1
§1.2.
Topological operations on topological spaces
4
§1.3.
Compactness.
7
Chapter
2.
Homotopy groups and homotopy equivalence
9
§2.1.
The fundamental group of a topological space
10
§2.2.
Higher homotopy groups
12
Chapter
3.
Coverings
21
Chapter
4.
Cell spaces (CW-complexes)
25
§4.1.
Definition and main properties of cell spaces
26
§4.2.
Classification of coverings
31
Chapter
5.
Relative homotopy groups and the exact sequence
of a pair
35
Chapter
6.
Fiber bundles
41
vii
viii Contents
§6.1.
Locally trivial bundles
41
§6.2.
The exact sequence of a fiber bundle
46
Chapter
7.
Smooth manifolds
49
§7.1.
Smooth structures
50
§7.2.
Orientations
52
§7.3.
Tangent bundles over smooth manifolds
53
§7.4.
Riemannian structures
55
Chapter
8.
The degree of a map
59
§8.1.
Critical sets of smooth maps
59
§8.2.
The degree of a map
60
§8.3.
The classification of maps Mn
->
Sn
63
§8.4.
The index of a vector field
66
Chapter
9.
Homology: Basic definitions and examples
69
§9.1.
Chain complexes and their homology
69
§9.2.
Simplicial homology of simplicial polyhedra
71
§9.3.
Maps of complexes
78
§9.4.
Singular homology
79
Chapter
10.
Main properties of singular homology groups and
their computation
83
§10.1.
Homology of the point
83
§10.2.
The exact sequence of a pair
84
§10.3.
The exact sequence of a triple
88
§10.4.
Homology of suspensions
89
§10.5.
The Mayer-Vietoris sequence
90
§10.6.
Homology of wedges
92
Contents ix
§10.7. Functoriality
of homology
92
§10.8.
Summary
93
Chapter
11. Homology
of cell spaces
95
§11.1.
Cellular complexes
95
§11.2.
Example: homology of
projective
spaces
97
§11.3.
Cell decomposition of
Grassmann
manifolds
98
Chapter
12.
Morse theory
103
§12.1.
Morse functions
103
§12.2.
The cellular structure of a manifold endowed with a
Morse function
104
§12.3.
Attaching handles
106
§12.4.
Regular Morse functions
106
§12.5.
The boundary operator in a Morse complex
110
§12.6.
Morse inequalities
114
§12.7.
Standard bifurcations of Morse functions
115
Chapter
13.
Cohomology and
Poincaré
duality
119
§13.1.
Cohomology
119
§13.2.
Poincaré
duality for manifolds without boundary
122
§13.3.
Manifolds with boundary and noncompact manifolds
124
§13.4.
Nonorientable manifolds
125
§13.5.
Alexander duality
126
Chapter
14.
Some applications of homology theory
129
§14.1.
The
Hopf
invariant
129
§14.2.
The degree of a map
131
§14.3.
The total index of a vector field equals the
Euler
characteristic
132
χ
Contents
Chapter
15.
Multiplication in cohomology (and homology)
137
§15.1.
Homology and cohomology groups of a Cartesian
product
137
§15.2.
Multiplication in cohomology
140
§15.3.
Examples of multiplication in cohomology
and its geometric meaning
142
§15.4.
Main properties of multiplication
in cohomology
143
§15.5.
Connection with the
de Rham
cohomology
144
§15.6.
Pontryagin multiplication
144
Index of Notations
145
Subject Index
147
|
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| author | Vasilʹev, Vjačeslav A. |
| author2 | Sossinsky, A. B. 1937- |
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| author_sort | Vasilʹev, Vjačeslav A. |
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| ctrlnum | (OCoLC)45799362 (DE-599)BVBBV013875994 |
| dewey-full | 514 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514 |
| dewey-search | 514 |
| dewey-sort | 3514 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013875994 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:53:37Z |
| institution | BVB |
| isbn | 0821821628 9780821821626 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009492655 |
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| physical | xiii, 149 Seiten Illustrationen, Diagramme |
| publishDate | 2001 |
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| publisher | American Mathematical Society |
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| series | Student mathematical library |
| series2 | Student mathematical library |
| spelling | Vasilʹev, Vjačeslav A. Verfasser (DE-588)120817896 aut Vvedenie v topologiju Introduction to topology V. A. Vassiliev. Translated by A. Sossinski Providence, Rhode Island American Mathematical Society [2001] © 2001 xiii, 149 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Student mathematical library volume 14 Algebraïsche topologie gtt Topologie Topology Topologie (DE-588)4060425-1 gnd rswk-swf Topologie (DE-588)4060425-1 s DE-604 Sossinsky, A. B. 1937- (DE-588)122444817 trl Erscheint auch als Online-Ausgabe 978-1-4704-2130-4 Student mathematical library volume 14 (DE-604)BV013184751 14 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009492655&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vasilʹev, Vjačeslav A. Introduction to topology Student mathematical library Algebraïsche topologie gtt Topologie Topology Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4060425-1 |
| title | Introduction to topology |
| title_alt | Vvedenie v topologiju |
| title_auth | Introduction to topology |
| title_exact_search | Introduction to topology |
| title_full | Introduction to topology V. A. Vassiliev. Translated by A. Sossinski |
| title_fullStr | Introduction to topology V. A. Vassiliev. Translated by A. Sossinski |
| title_full_unstemmed | Introduction to topology V. A. Vassiliev. Translated by A. Sossinski |
| title_short | Introduction to topology |
| title_sort | introduction to topology |
| topic | Algebraïsche topologie gtt Topologie Topology Topologie (DE-588)4060425-1 gnd |
| topic_facet | Algebraïsche topologie Topologie Topology |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009492655&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013184751 |
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