Elements of homotopy theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York [u.a.]
Springer
1995
|
| Edition: | Corr. 3. printing |
| Series: | Graduate texts in mathematics
61 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 728 - 735 |
| Physical Description: | XXI, 744 S. graph. Darst. |
| ISBN: | 3540903364 0387903364 |
Staff View
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| 100 | 1 | |a Whitehead, George W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Elements of homotopy theory |c George W. Whitehead |
| 250 | |a Corr. 3. printing | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1995 | |
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| 490 | 1 | |a Graduate texts in mathematics |v 61 | |
| 500 | |a Literaturverz. S. 728 - 735 | ||
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Record in the Search Index
| _version_ | 1807323811056451584 |
|---|---|
| adam_text |
CONTENTS
CHAPTER
I
INTRODUCTORY
NOTIONS
1
1.
THE
FUNDAMENTAL
PROBLEMS:
EXTENSION,
HOMOTOPY,
AND
CLASSIFICATION
3
2.
STANDARD
NOTATIONS
AND
CONVENTIONS
9
3.
MAPS
OF
THE
N-SPHERE
INTO
ITSELF
13
4.
COMPACTLY
GENERATED
SPACES
17
5.
NDR-PAIRS
21
6.
FILTERED
SPACES
27
7.
FIBRATIONS
29
CHAPTER
II
CW-COMPLEXES
46
1.
CONSTRUCTION
OF
CW-COMPLEXES
48
2.
HOMOLOGY
THEORY
OF
CW-COMPLEXES
54
3.
COMPRESSION
THEOREMS
70
4.
CELLULAR
MAPS
76
5.
LOCAL
CAICULATIONS
79
6.
REGULAR
CELL
COMPLEXES
81
7.
PRODUCTS
AND
THE
COHOMOLOGY
RING
88
CHAPTER
III
GENERALITIES
ON
HOMOTOPY
CLASSES
OF
MAPPINGS
96
1.
HOMOTOPY
AND
THE
FUNDAMENTAL
GROUP
98
2.
SPACES
WITH
BASE
POINTS
102
XVIII
CONTENTS
3.
GROUPS
OF
HOMOTOPY
CLASSES
115
4.
H-SPACES
116
5.
H'-SPACES
121
6.
EXACT
SEQUENCES
OF
MAPPING
FUNCTORS
127
7.
HOMOLOGY
PROPERTIES
OF
H-SPACES
AND
H'-SPACES
142
8.
HOPF
ALGEBRAS
149
CHAPTER
IV
HOMOTOPY
GROUPS
157
1.
RELATIVE
HOMOTOPY
GROUPS
158
2.
THE
HOMOTOPY
SEQUENCE
161
3.
THE
OPERATIONS
OF
THE
FUNDAMENTAL
GROUP
ON
THE
HOMOTOPY
SEQUENCE
164
4.
THE
HUREWICZ
MAP
166
5.
THE
EILENBERG
AND
BLAKERS
HOMOLOGY
GROUPS
170
6.
THE
HOMOTOPY
ADDITION
THEOREM
174
7.
THE
HUREWICZ
THEOREMS
178
8.
HOMOTOPY
RELATIONS
IN
FIBRE
SPACES
185
9.
FIBRATIONS
IN
WHICH
THE
BASE
OR
FIBRE
IS
A
SPHERE
194
10.
ELEMENTARY
HOMOTOPY
THEORY
OF
LIE
GROUPS
AND
THEIR
COSET
SPACES
196
CHAPTER
V
HOMOTOPY
THEORY
OF
CW-COMPLEXES
209
1.
THE
EFFECT
ON
THE
HOMOTOPY
GROUPS
OF
A
CELLULAR
EXTENSION
211
2.
SPACES
WITH
PRESCRIBED
HOMOTOPY
GROUPS
216
3.
WEAK
HOMOTOPY
EQUIVALENCE
AND
CW-APPROXIMATION
219
4.
ASPHERICAL
SPACES
224
5.
OBSTRUCTION
THEORY
228
6.
HOMOTOPY
EXTENSION
AND
CLASSIFICATION
THEOREMS
235
7.
EILENBERG-MAC
LANE
SPACES
244
8.
COHOMOLOGY
OPERATIONS
250
CHAPTER
VI
HOMOLOGY
WITH
LOCAL
COEFFICIENTS
255
1.
BUNDLES
OF
GROUPS
257
2.
HOMOLOGY
WITH
LOCAL
COEFFICIENTS
265
3.
COMPUTATIONS
AND
EXAMPLES
275
4.
LOCAL
COEFFICIENTS
IN
CW-COMPLEXES
281
5.
OBSTRUCTION
THEORY
IN
FIBRE
SPACES
291
6.
THE
PRIMARY
OBSTRUCTION
TO
A
LIFTING
297
7.
CHARACTERISTIC
CLASSES
OF
VECTOR
BUNDLES
305
CONTENTS
XIX
CHAPTER
VII
HOMOLOGY
OF
FIBRE
SPACES:
ELEMENTARY
THEORY
314
L
FIBRATIONS
OVER
A
SUSPENSION
316
2.
THE
JAMES
REDUCED
PRODUCTS
326
3.
FUERTHER
PROPERTIES
OF
THE
WANG
SEQUENCE
336
4.
HOMOLOGY
OF
THE
CLASSICAL
GROUPS
341
5.
FIBRATIONS
HAVING
A
SPHERE
AS
FIBRE
349
6.
THE
HOMOLOGY
SEQUENCE
OF
A
FIBRATION
363
7.
THE
BLAKERS-MASSEY
HOMOTOPY
EXCISION
THEOREM
366
CHAPTER
VIII
THE
HOMOLOGY
SUSPENSION
371
1.
THE
HOMOLOGY
SUSPENSION
373
2.
PROOF
OF
THE
SUSPENSION
THEOREM
379
3.
APPLICATIONS
382
4.
COHOMOLOGY
OPERATIONS
385
5.
STABLE
OPERATIONS
390
6.
THE
MOD
2
STEENROD
ALGEBRA
394
7.
THE
CARTAN
PRODUCT
FORMULA
397
8.
SOME
RELATIONS
AMONG
THE
STEENROD
SQUARES
403
9.
THE
ACTION
OF
THE
STEENROD
ALGEBRA
ON
THE
COHOMOLOGY
OF
SOME
COMPACT
LIE
GROUPS
408
CHAPTER
IX
POSTNIKOV
SYSTEMS
415
1.
CONNECTIVE
FIBRATIONS
417
2.
THE
POSTNIKOV
INVARIANTS
OF
A
SPACE
421
3.
AMPLIFYING
A
SPACE
BY
A
COHOMOLOGY
CLASS
426
4.
RECONSTRUCTION
OF
A
SPACE
FROM
ITS
POSTNIKOV
SYSTEM
430
5.
SOME
EXAMPLES
437
6.
RELATIVE
POSTNIKOV
SYSTEMS
443
7.
POSTNIKOV
SYSTEMS
AND
OBSTRACTION
THEORY
449
CHAPTER
X
ON
MAPPINGS
INTO
GROUP-LIKE
SPACES
456
1.
THE
CATEGORY
OF
A
SPACE
457
2.
H
0
-SPACES
461
3.
NILPOTENCY
OF
[X,
G]
462
4.
THE
CASE
X
=
XJ
X
YY
X
X
K
465
5.
THE
SAMELSON
PRODUCT
467
6.
COMMUTATORS
AND
HOMOLOGY
470
7.
THE
WHITEHEAD
PRODUCT
472
8.
OPERATIONS
IN
HOMOTOPY
GROUPS
478
XX
CONTENTS
CHAPTER
XI
HOMOTOPY
OPERATIONS
488
1.
HOMOTOPY
OPERATIONS
490
2.
THE
HOPF
INVARIANT
494
3.
THE
FUNCTIONAL
CUP
PRODUCT
496
4.
THE
HOPF
CONSTRUCTION
502
5.
GEOMETRICAL
INTERPRETATION
OF
THE
HOPF
INVARIANT
507
6.
THE
HILTON-MILNOR
THEOREM
511
7.
PROOF
OF
THE
HILTON-MILNOR
THEOREM
515
8.
THE
HOPF-HILTON
INVARIANTS
533
CHAPTER
XII
STAHLE
HOMOTOPY
AND
HOMOLOGY
542
1.
HOMOTOPY
PROPERTIES
OF
THE
JAMES
IMBEDDING
544
2.
SUSPENSION
AND
WHITEHEAD
PRODUCTS
546
3.
THE
SUSPENSION
CATEGORY
550
4.
GROUP
EXTENSIONS
AND
HOMOLOGY
561
5.
STAHLE
HOMOTOPY
AS
A
HOMOLOGY
THEORY
571
6.
COMPARISON
WITH
THE
EILENBERG-STEENROD
AXIOMS
578
7.
COHOMOLOGY
THEORIES
594
CHAPTER
XIII
HOMOLOGY
OF
FIBRE
SPACES
602
1.
THE
HOMOLOGY
OF
A
FILTERND
SPACE
604
2.
EXACT
COUPLES
609
3.
THE
EXACT
COUPLES
OF
A
FILTERED
SPACE
613
4.
THE
SPECTRAL
SEQUENCE
OF
A
FIBRATION
623
5.
PROOFS
OF
THEOREMS
(4.7)
AND
4.8)
632
6.
THE
ATIYAH-HIRZEBRUCH
SPECTRAL
SEQUENCE
640
7.
THE
LERAY-SERRE
SPECTRAL
SEQUENCE
645
8.
MULTIPLICATIVE
PROPERTIES
OF
THE
LERAY-SERRE
SPECTRAL
SEQUENCE
654
9.
FUERTHER
APPLICATIONS
OF
THE
LERAY-SERRE
SPECTRAL
SEQUENCE
668
APPENDIX
A
COMPACT
LIE
GROUPS
673
1.
SUBGROUPS,
COSET
SPACES,
MAXIMAL
TORI
674
2.
CLASSIFYING
SPACES
678
3.
THE
SPINOR
GROUPS
680
4.
THE
CAYLEY
ALGEBRA
K
686
5.
AUTOMORPHISMS
OF
K
690
6.
THE
EXCEPTIONAL
JORDAN
ALGEBRA
3
695
7.
THE
EXCEPTIONAL
LIE
GROUP
F
4
701
CONTENTS
XXI
APPENDIX
B
ADDITIVE
RELATIONS
716
1.
DIRECT
SUMS
AND
PRODUCTS
717
2.
ADDITIVE
RELATIONS
722
BIBLIOGRAPHY
728
INDEX
737 |
| any_adam_object | 1 |
| author | Whitehead, George W. |
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| ctrlnum | (OCoLC)34318257 (DE-599)BVBBV010669833 |
| dewey-full | 514/.24 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.24 |
| dewey-search | 514/.24 |
| dewey-sort | 3514 224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Corr. 3. printing |
| format | Book |
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| genre_facet | Einführung |
| id | DE-604.BV010669833 |
| illustrated | Illustrated |
| indexdate | 2024-08-14T01:18:18Z |
| institution | BVB |
| isbn | 3540903364 0387903364 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007122393 |
| oclc_num | 34318257 |
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| owner_facet | DE-355 DE-BY-UBR DE-91 DE-BY-TUM DE-11 |
| physical | XXI, 744 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Whitehead, George W. Verfasser aut Elements of homotopy theory George W. Whitehead Corr. 3. printing New York [u.a.] Springer 1995 XXI, 744 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 61 Literaturverz. S. 728 - 735 Homotopy theory Homotopie (DE-588)4025803-8 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Homotopietheorie (DE-588)4128142-1 s DE-604 Homotopie (DE-588)4025803-8 s 2\p DE-604 Graduate texts in mathematics 61 (DE-604)BV000000067 61 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007122393&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Whitehead, George W. Elements of homotopy theory Graduate texts in mathematics Homotopy theory Homotopie (DE-588)4025803-8 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (DE-588)4025803-8 (DE-588)4128142-1 (DE-588)4151278-9 |
| title | Elements of homotopy theory |
| title_auth | Elements of homotopy theory |
| title_exact_search | Elements of homotopy theory |
| title_full | Elements of homotopy theory George W. Whitehead |
| title_fullStr | Elements of homotopy theory George W. Whitehead |
| title_full_unstemmed | Elements of homotopy theory George W. Whitehead |
| title_short | Elements of homotopy theory |
| title_sort | elements of homotopy theory |
| topic | Homotopy theory Homotopie (DE-588)4025803-8 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Homotopy theory Homotopie Homotopietheorie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007122393&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT whiteheadgeorgew elementsofhomotopytheory |