Algebraic topology:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1995
|
| Ausgabe: | 3., corr. print. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 528 S. |
| ISBN: | 0387944265 0387906460 3540906460 |
Internformat
MARC
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| 100 | 1 | |a Spanier, Edwin Henry |d 1921-1996 |e Verfasser |0 (DE-588)11565819X |4 aut | |
| 245 | 1 | 0 | |a Algebraic topology |c Edwin H. Spanier |
| 250 | |a 3., corr. print. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1995 | |
| 300 | |a XIV, 528 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Algebraische Topologie |0 (DE-588)4120861-4 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-014154521 | ||
Datensatz im Suchindex
| _version_ | 1804134535283081216 |
|---|---|
| adam_text | CONTENTS
INTRODUCTION I
1
Set theory
1
2
General topology
4
3
Group theory
6
4
Modules
7
5
Euclidean spaces
9
1
HOMOTOPV AND THE
FUNDAMENTAL
GROUP IS
1
Categories
14
2
Functors
18
3
Homotopy
22
4
Retraction and deformation
27
5
Hspaces
33
β
Suspension
39
7
The fundamental groupoid
45
8
The fundamental group
50
Exercises
56
xi
xii
contents
2 COVERIN« SPACES AN»
VIBRATIONS
·Ο
1
Covering projections
62
2
The homotopy Ufting property
65
3
Relations with the fundamental group
70
4
The lifting problem
74
5
The classification of covering projections
79
6
Covering transformations
85
7
Fiber bundles
89
8
Fibrattons
96
Exercises
103
POLVHEDBA
1·β
1
Simplicial complexes
108
2
Linearity in simplicial complexes
114
3
Subdivision
121
4
Simplicial approximation
126
5
Contiguity classes
129
β
The edge-pefh groupoid
134
7
Graphs
139
8
Examples and applications
143
Exercises
149
HOMOLOG
Y
184
1
Chain complexes
156
2
Chain homotopy
162
3
The homohgy of simplicial complexes
167
4
Singular homohgy
173
5
Exactness
179
β
Mayer-Vietoris sequences
186
7
Some applications of homohgy
193
8
Axiomatic characterization of homohgy
199
Exercises
205
CONTENTS
ХІІІ
5
PRODUCTS
21β
1
Homology with coefficients
212
2
The universal-coefficient theorem, for homohgy
219
3
The
Künneth
formula
227
4
Cohomohgy
236
6
The universal-coefficient theorem, for cohomohgy
241
β
Cup and cap products
248
7
Homology of fiber bundles
255
8
The cohomohgy algebra
263
О
The Steenrod squaring operations
269
Exercises
276
6
GENERAL COBOMOLOSY THEORY AN» DUALITY
3*4
1
The slant product
286
2
Duality in topohgical manifolds
292
3
The fundamental class of a manifold
299
4
The Alexander cohomology theory
306
5
The homotopy axiom for the Alexander theory
311
β
Tautness and continuity
315
7
Presheaves
323
8
Fine presheaves
329
9
Applications of the
cóhomology
of presheaves
338
10
Characteristic classes
346
Exercises
356
HOMOTOPY THEORY 3«3
1
Exact sequences of sets of homotopy classes
364
2
Higher homotopy groups
371
3
Change of base points
379
4
The Hurewicz homomorphism
387
5
The Hurewicz isomorphism theorem
393
β
CWcomplexes
400
7
Homotopy functors
406
Я
Weak homotopy type
412
Exercise»
418
MV
CONTENTS
8
OBSTRUCTION THEORY
423
1 EÜenberg-MacLane
spaces
424
2
Principal fibrations
432
3
Moore-Postnikov factorizations
437
4
Obstruction theory
445
5
The suspension map
452
Exercises
4вО
€F SPECTRAL SEQUENCES AND HOMOTOPV
GROUPS OF SPHERES
4«4
1
Spectral sequences
466
2
The spectral sequence of a fibration
473
3
Applications of the homoiogy spectral sequence
481
4
Multiplicative properties of spectral sequences
490
5
Applications of the cohomology spectral sequence
498
β
Sen« classes of abelian groups
504
7
Homotopy groups of spheres
512
Exercises
518
INDEX SSI
|
| adam_txt |
CONTENTS
INTRODUCTION I
1
Set theory
1
2
General topology
4
3
Group theory
6
4
Modules
7
5
Euclidean spaces
9
1
HOMOTOPV AND THE
FUNDAMENTAL
GROUP IS
1
Categories
14
2
Functors
18
3
Homotopy
22
4
Retraction and deformation
27
5
Hspaces
33
β
Suspension
39
7
The fundamental groupoid
45
8
The fundamental group
50
Exercises
56
xi
xii
contents
2 COVERIN« SPACES AN»
VIBRATIONS
·Ο
1
Covering projections
62
2
The homotopy Ufting property
65
3
Relations with the fundamental group
70
4
The lifting problem
74
5
The classification of covering projections
79
6
Covering transformations
85
7
Fiber bundles
89
8
Fibrattons
96
Exercises
103
POLVHEDBA
1·β
1
Simplicial complexes
108
2
Linearity in simplicial complexes
114
3
Subdivision
121
4
Simplicial approximation
126
5
Contiguity classes
129
β
The edge-pefh groupoid
134
7
Graphs
139
8
Examples and applications
143
Exercises
149
HOMOLOG
Y
184
1
Chain complexes
156
2
Chain homotopy
162
3
The homohgy of simplicial complexes
167
4
Singular homohgy
173
5
Exactness
179
β
Mayer-Vietoris sequences
186
7
Some applications of homohgy
193
8
Axiomatic characterization of homohgy
199
Exercises
205
CONTENTS
ХІІІ
5
PRODUCTS
21β
1
Homology with coefficients
212
2
The universal-coefficient theorem, for homohgy
219
3
The
Künneth
formula
227
4
Cohomohgy
236
6
The universal-coefficient theorem, for cohomohgy
241
β
Cup and cap products
248
7
Homology of fiber bundles
255
8
The cohomohgy algebra
263
О
The Steenrod squaring operations
269
Exercises
276
6
GENERAL COBOMOLOSY THEORY AN» DUALITY
3*4
1
The slant product
286
2
Duality in topohgical manifolds
292
3
The fundamental class of a manifold
299
4
The Alexander cohomology theory
306
5
The homotopy axiom for the Alexander theory
311
β
Tautness and continuity
315
7
Presheaves
323
8
Fine presheaves
329
9
Applications of the
cóhomology
of presheaves
338
10
Characteristic classes
346
Exercises
356
HOMOTOPY THEORY 3«3
1
Exact sequences of sets of homotopy classes
364
2
Higher homotopy groups
371
3
Change of base points
379
4
The Hurewicz homomorphism
387
5
The Hurewicz isomorphism theorem
393
β
CWcomplexes
400
7
Homotopy functors
406
Я
Weak homotopy type
412
Exercise»
418
MV
CONTENTS
8
OBSTRUCTION THEORY
423
1 EÜenberg-MacLane
spaces
424
2
Principal fibrations
432
3
Moore-Postnikov factorizations
437
4
Obstruction theory
445
5
The suspension map
452
Exercises
4вО
€F SPECTRAL SEQUENCES AND HOMOTOPV
GROUPS OF SPHERES
4«4
1
Spectral sequences
466
2
The spectral sequence of a fibration
473
3
Applications of the homoiogy spectral sequence
481
4
Multiplicative properties of spectral sequences
490
5
Applications of the cohomology spectral sequence
498
β
Sen« classes of abelian groups
504
7
Homotopy groups of spheres
512
Exercises
518
INDEX SSI |
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| author | Spanier, Edwin Henry 1921-1996 |
| author_GND | (DE-588)11565819X |
| author_facet | Spanier, Edwin Henry 1921-1996 |
| author_role | aut |
| author_sort | Spanier, Edwin Henry 1921-1996 |
| author_variant | e h s eh ehs |
| building | Verbundindex |
| bvnumber | BV020832542 |
| classification_rvk | SK 300 |
| ctrlnum | (OCoLC)246929499 (DE-599)BVBBV020832542 |
| dewey-full | 514/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.2 |
| dewey-search | 514/.2 |
| dewey-sort | 3514 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 3., corr. print. |
| format | Book |
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| id | DE-604.BV020832542 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T13:13:42Z |
| indexdate | 2024-07-09T20:26:09Z |
| institution | BVB |
| isbn | 0387944265 0387906460 3540906460 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014154521 |
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| physical | XIV, 528 S. |
| publishDate | 1995 |
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| spelling | Spanier, Edwin Henry 1921-1996 Verfasser (DE-588)11565819X aut Algebraic topology Edwin H. Spanier 3., corr. print. New York [u.a.] Springer 1995 XIV, 528 S. txt rdacontent n rdamedia nc rdacarrier Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Algebraische Topologie (DE-588)4120861-4 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014154521&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Spanier, Edwin Henry 1921-1996 Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4120861-4 (DE-588)4123623-3 |
| title | Algebraic topology |
| title_auth | Algebraic topology |
| title_exact_search | Algebraic topology |
| title_exact_search_txtP | Algebraic topology |
| title_full | Algebraic topology Edwin H. Spanier |
| title_fullStr | Algebraic topology Edwin H. Spanier |
| title_full_unstemmed | Algebraic topology Edwin H. Spanier |
| title_short | Algebraic topology |
| title_sort | algebraic topology |
| topic | Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | Algebraische Topologie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014154521&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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