Introduction to homotopy theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[1997]
|
| Series: | Fields Institute for Research in Mathematical Sciences <Toronto>: Fields Institute monographs
9 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxi, 188 Seiten |
| ISBN: | 0821806904 9780821844366 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text |
Contents
Preface
xi
Summary of Global Notation
xv
Part I
-
Prerequisites
1
Chapter
1
Prerequisites from Category Theory
3
1
Definitions
3
2
Universal Constructions
4
3
Basic Notions from Categorical Theory
5
Chapter
2
Prerequisites from Point Set Topology
7
1
Definitions and Elementary Constructions
7
2
Separation
8
3
Compactness
9
4
Connectedness
10
5
Coverings and Paracompactness
10
6
Coherent and Compactly Generated Topologies
11
7
CW-complexes
12
Chapter
3
The Fundamental Group
15
1
Homotopy
15
2
Covering Spaces
17
3
Van Kampen's Theorem
20
Chapter
4
Homological Algebra
21
1
Chain Complexes
21
2
Direct Limits
24
3
Derived Functors
25
4
Tensor Products, Duals, and Universal Coefficient Theorems
28
5
Adjoint Functors
30
6
Relative Derived Functors
30
7
Derived Functors of
lim 31
Chapter
5
Homology of Spaces
33
1
Eilenberg-Steenrod Homology Axioms
33
2
Singular Homology Theory
34
3
Homology Calculations and Elementary Applications
38
4
Homology of CW-complexes; Cellular Homology
39
5
Acyclic Models
41
6
Singular Cohomology
43
7
Relative Cohomology
44
viii Contents
Chapter
6
Manifolds
47
1
Definitions
47
2
Orientation on Manifolds
47
3
Poincaré
Duality
48
Part II
-
Homotopy Theory
51
Chapter
7
Higher Homotopy Theory
53
1
Fibrations and Cofibrations
53
2
Group Structures on Sets of Homotopy Classes
62
3
Homology of a Loop-suspension
66
4
Relation between Homotopy Groups and Homology Groups
67
5
Reduction to the Case of Simply Connected CW-Complexes
72
6
Diagrams of Exact Homotopy Sequences
76
7
Ganea's Theorem
81
8
Whitehead and Samelson Products
83
9
James Construction
84
10
Lusternik-Schnirrelmann Category
88
Chapter
8
Simplicial Sets
89
1
Definitions and First Principles
89
2
Simplicial Fibrations and Kan Complexes
92
3
Simplicial Groups
94
4
The Singular Complex
94
5
Simplicial Abelian Groups
95
6
Simplicial Approximation
97
Chapter
9
Fibre Bundles and Classifying Spaces
99
1
Fibre Bundles
99
2
Classifying Principal Bundles and Milnor's Construction
100
Chapter
10 Hopf
Algebras and Graded Lie Algebras
105
1
Algebras and
Coalgebras
105
2
Tensor Products and Cotensor Products
107
3
Kernels and Cokernels
107
4
Primitives and
Indécomposables
109
5
Graded Lie Algebras
109
6
The Canonical Conjugation
110
Chapter
11
Spectral Sequences
113
1
Filtrations
113
2
Definition of Spectral Sequence
114
3
Exact Couples
116
4
Exact Couple of a Filtered Object
119
5
Bigraded Spectral Sequences
121
6
Multiplicative Spectral Sequences
122
Contents ix
7
Spectral
Sequence of a Double Complex
123
8 Bockstein
Spectral Sequence
125
9
Serre
Spectral Sequence
126
10
Adams-Hilton Models
136
11
Eilenberg-Moore Spectral Sequence
141
12
Grothendieck Spectral Sequence
145
Chapter
12
Localization and Completion
147
1
Triples and Cotriples
147
2
The Bousfield-Kan Construction
147
Chapter
13
Generalized Homology and Stable Homotopy
153
1
Generalized Homology
153
2
Stable Homotopy Groups
156
3
Spectra
156
4
Eilenberg-MacLane Spaces and Brown Represent ability
158
Chapter
14
Cohomology Operations and the Steenrod Algebra
161
1
Primary Cohomology Operations
161
2
The Steenrod Algebra as
a
Hopf
Algebra
162
3
Construction of the Steenrod Reduced Power Operations
163
4
Calculation of the Steenrod Algebra
170
5
Dual of the Steenrod Algebra
174
6
Sample Applications of the Steenrod Algebra
175
7
Secondary Cohomology Operations
179
Bibliography
181
Index
183 |
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-08-20T00:26:38Z |
| institution | BVB |
| isbn | 0821806904 9780821844366 |
| language | English |
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| physical | xxi, 188 Seiten |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Fields Institute for Research in Mathematical Sciences <Toronto>: Fields Institute monographs |
| series2 | Fields Institute for Research in Mathematical Sciences <Toronto>: Fields Institute monographs |
| spelling | Selick, Paul 1950- Verfasser (DE-588)173130704 aut Introduction to homotopy theory Paul Selick Providence, Rhode Island American Mathematical Society [1997] © 1997 xxi, 188 Seiten txt rdacontent n rdamedia nc rdacarrier Fields Institute for Research in Mathematical Sciences <Toronto>: Fields Institute monographs 9 Homotopie (DE-588)4025803-8 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Homotopie (DE-588)4025803-8 s DE-604 Homotopietheorie (DE-588)4128142-1 s Erscheint auch als Online-Ausgabe 978-1-4704-3136-5 Fields Institute for Research in Mathematical Sciences <Toronto>: Fields Institute monographs 9 (DE-604)BV009737926 9 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007754873&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Selick, Paul 1950- Introduction to homotopy theory Fields Institute for Research in Mathematical Sciences <Toronto>: Fields Institute monographs Homotopie (DE-588)4025803-8 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (DE-588)4025803-8 (DE-588)4128142-1 (DE-588)4123623-3 |
| title | Introduction to homotopy theory |
| title_auth | Introduction to homotopy theory |
| title_exact_search | Introduction to homotopy theory |
| title_full | Introduction to homotopy theory Paul Selick |
| title_fullStr | Introduction to homotopy theory Paul Selick |
| title_full_unstemmed | Introduction to homotopy theory Paul Selick |
| title_short | Introduction to homotopy theory |
| title_sort | introduction to homotopy theory |
| topic | Homotopie (DE-588)4025803-8 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Homotopie Homotopietheorie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007754873&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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