Introduction to homotopy theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2011
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIII, 344 S. graph. Darst. |
| ISBN: | 9781441973283 |
Staff View
MARC
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| 100 | 1 | |a Arkowitz, Martin |d 1935- |e Verfasser |0 (DE-588)107714361 |4 aut | |
| 245 | 1 | 0 | |a Introduction to homotopy theory |c Martin Arkowitz |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2011 | |
| 300 | |a XIII, 344 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1805145321431367680 |
|---|---|
| adam_text |
Contents
Basic Homotopy. 1
1.1
Introduction
. 1
1.2 Spaces.
Maps.
Products, and
Wedges
. 2
1.3 Homotopy
I
. .4
1.4 Homotopy
II
. 7
1.5 C'W
Complexos
. 18
Iti
Why Study Homotopy Theory?
. 29
Exercises
.
.'íl
Н
-Spaces and Co-H-Spaces
. 35
2.1
Introduction
. 35
2.2
Н
-Spaces and Co-H-Spaces
. 36
2.3
Loop Spaces and Suspensions
. 44
2.4
Homotopy Groups I
. 50
2.5
Moore Spaces and Eilenberg-Mac Lane Spaces
. 60
2.6
Eckmann-Hilton Duality I
. 67
Exercises
. 70
Coñbrations
and Fibrations
. 75
3.1
Introduction
. 75
3.2
Cofibrations
. 75
3.3
Fibrations
. 83
3.4
Examples of Fiber Bundles
. 93
3.5
Replacing a Map by a Cofiber or Fiber Map
.104
Exercises
.109
Exact Sequences
.115
4.1
Introduction
.115
4.2
The Coexact and Exact Sequence of a Map
.116
4.3
Actions and Coactions
.125
4.4
Operations
.130
xii Contents
4.5
Homotopy Groups II
.135
Exercises
.150
5
Applications of Exactness
.155
5.1
Introduction
.155
5.2
Universal Coefficient Theorems
.156
5.3
Homotopical Cohomology Groups
.160
5.4
Applications to Fiber and Cofiber Sequences
.163
5.5
The Operation of the Fundamental Group
.169
5.6
Calculation of Homotopy Groups
.177
Exercises
.190
6
Homotopy Pushouts and Pullbacks
.195
6.1
Introduction
.195
6.2
Homotopy Pushouts and Pullbacks I
.196
6.3
Homotopy Pushouts and Pullbacks II
.207
6.4
Theorems of
Serre,
Hurewicz, and Blakers-Massey
.214
6.5
Eckmann-Hilton Duality II
.225
Exercises
.227
7
Homotopy and Homology Decompositions
.233
7.1
Introduction
.233
7.2
Homotopy Decompositions of Spaces
.234
7.3
Homology Decompositions of Spaces
.247
7.4
Homotopy and Homology Decompositions of Maps
.254
Exercises
.264
8
Homotopy Sets
.267
8.1
Introduction
.267
8.2
The Set [X,Y]
.267
8.3
Category
.270
8.4
Loop and Group Structure in [X, Y]
.275
Exercises
.279
9
Obstruction Theory
.283
9.1
Introduction
.283
9.2
Obstructions Using Homotopy Decompositions
.284
9.3
Lifts and Extensions
.288
9.4
Obstruction Miscellany
.291
Exercises
.296
A Point-Set Topology
.299
В
The Fundamental Group
.303
С
Homology and Cohomology
.307
Contents xiii
D
Homotopy
Groups of the
η
-Sphere.
312
E
Homotopy Pushouts and
Pułlbacks
.314
Ρ
Categories and Functors
.323
Hints to Some of the Exercises
.329
References
.335
Index
.339 |
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| indexdate | 2024-07-21T00:12:10Z |
| institution | BVB |
| isbn | 9781441973283 |
| language | English |
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| physical | XIII, 344 S. graph. Darst. |
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| spelling | Arkowitz, Martin 1935- Verfasser (DE-588)107714361 aut Introduction to homotopy theory Martin Arkowitz New York [u.a.] Springer 2011 XIII, 344 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Homotopietheorie (DE-588)4128142-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Homotopietheorie (DE-588)4128142-1 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4419-7329-0 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3495816&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024475074&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arkowitz, Martin 1935- Introduction to homotopy theory Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (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 Martin Arkowitz |
| title_fullStr | Introduction to homotopy theory Martin Arkowitz |
| title_full_unstemmed | Introduction to homotopy theory Martin Arkowitz |
| title_short | Introduction to homotopy theory |
| title_sort | introduction to homotopy theory |
| topic | Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Homotopietheorie Lehrbuch |
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