Lectures on algebraic topology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin u.a.
Springer
1995
|
| Edition: | Reprint of the 1980 ed. |
| Series: | Classics in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Früher als: Grundlehren der mathematischen Wissenschaften ; 200 Weitere Ausgabe: Grundlehren der mathematischen Wissenschaften ; 200 |
| Physical Description: | XI, 377 S. graph. Darst. |
| ISBN: | 3540586601 |
Staff View
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| 100 | 1 | |a Dold, Albrecht |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Lectures on algebraic topology |c Albrecht Dold |
| 250 | |a Reprint of the 1980 ed. | ||
| 264 | 1 | |a Berlin u.a. |b Springer |c 1995 | |
| 300 | |a XI, 377 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Classics in mathematics | |
| 500 | |a Früher als: Grundlehren der mathematischen Wissenschaften ; 200 | ||
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Record in the Search Index
| _version_ | 1804124352875069440 |
|---|---|
| adam_text | A Dold
Lectures on Algebraic
Topology
With 10 Figures
Springer-Verlag
Berlin Heidelberg New York 1972
© 2008 AGI-Information Management Consultants
May be used for personal purporses only or by
libraries associated to dandelon com network
Contents
Chapter I
Chapter IV
Preliminaries on Categories,
Abelian Groups, and Homotopy
§ 1 Categories and Functors
§ 2 Abelian Groups (Exactness, Direct Sums,
Free Abelian Groups)
§ 3 Homotopy
Chapter II
Chapter III
§1
§2
§3
§4
Homology of Complexes
Complexes
Connecting Homomorphism,
Exact Homology Sequence
Chain-Homotopy
Free Complexes
Singular Homology
§ 1 Standard Simplices and Their Linear Maps
§ 2 The Singular Complex
§ 3 Singular Homology
§ 4 Special Cases
§ 5 Invariance under Homotopy
§ 6 Barycentric Subdivision
§ 7 Small Simplices Excision
§ 8 Mayer-Vietoris Sequences
Applications to Euclidean Space
§ 1 Standard Maps between Cells and Spheres
§ 2 Homology of Cells and Spheres
§ 3 Local Homology
§ 4 The Degree of a Map
§ 5 Local Degrees
§ 6 Homology Properties
of Neighborhood Retracts in JR
7
X Contents
§ 7 Jordan Theorem, Invariance of Domain 78
§ 8 Euclidean Neighborhood Retracts (ENRs) 79
Chapter V Cellular Decomposition
and Cellular Homology 85
§1 Cellular Spaces 85
§2 CW-Spaces 88
§ 3 Examples 95
§ 4 Homology Properties of CW-Spaces 101
§ 5 The Euler-Poincare Characteristic 104
§ 6 Description of Cellular Chain Maps and
of the Cellular Boundary Homomorphism 106
§ 7 Simplicial Spaces 111
§8 Simplicial Homology 119
Chapter VI Functors of Complexes 123
§1 Modules 123
§ 2 Additive Functors 127
§3 Derived Functors 132
§4 Universal Coefficient Formula 136
§ 5 Tensor and Torsion Products 140
§ 6 Horn and Ext 146
§ 7 Singular Homology and Cohomology
with General Coefficient Groups 150
§ 8 Tensorproduct and Bilinearity 157
§ 9 Tensorproduct of Complexes
Kunneth Formula 161
§ 10 Horn of Complexes
Homotopy Classification of Chain Maps 167
§11 Acyclic Models 174
§ 12 The Eilenberg-Zilber Theorem
Kunneth Formulas for Spaces 178
Chapter VII Products 186
§ 1 The Scalar Product 187
§ 2 The Exterior Homology Product 189
§ 3 The Interior Homology Product
(Pontrjagin Product) 193
§4 Intersection Numbers in R 197
§ 5 The Fixed Point Index 202
§ 6 The Lef schetz-Hopf Fixed Point
Theorem 207
§ 7 The Exterior Cohomology Product 214
Contents XI
§ 8 The Interior Cohomology Product
(—Product) 219
§ 9 --Products in Projective Spaces
Hopf Maps and Hopf Invariant 222
§10 Hopf Algebras 227
§ 11 The Cohomology Slant Product 233
§ 12 The Cap-Product (—Product) 238
§ 13 The Homology Slant Product,
and the Pontrjagin Slant Product 245
Chapter VIII Manifolds 247
§ 1 Elementary Properties of Manifolds 247
§2 The Orientation Bundle of a Manifold 251
§ 3 Homology of Dimensions ; n
in n-Manifolds 259
§ 4 Fundamental Class and Degree 266
§5 Limits 272
§ 6 tech Cohomology
of Locally Compact Subsets of R 281
§7 PoincareVLefschetz Duality 291
§ 8 Examples, Applications 298
§9 Duality in 5-Manifolds 303
§ 10 Transfer 308
§11 Thom Class, Thom Isomorphism 314
§ 12 The Gysin Sequence Examples 325
§ 13 Intersection of Homology Classes 335
Appendix Kan- and tech-Extensions of Functors 348
§ 1 Limits of Functors 348
§ 2 Polyhedrons under a Space,
and Partitions of Unity 352
§ 3 Extending Functors from Polyhedrons
to More General Spaces 361
Bibliography 368
Subject Index 371
|
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| dewey-full | 514/.220 |
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| dewey-ones | 514 - Topology |
| dewey-raw | 514/.2 20 |
| dewey-search | 514/.2 20 |
| dewey-sort | 3514 12 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Reprint of the 1980 ed. |
| format | Book |
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| id | DE-604.BV009978994 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:44:18Z |
| institution | BVB |
| isbn | 3540586601 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006613642 |
| oclc_num | 258093919 |
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| owner_facet | DE-384 DE-20 DE-29T DE-355 DE-BY-UBR DE-521 DE-83 DE-11 |
| physical | XI, 377 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| series2 | Classics in mathematics |
| spelling | Dold, Albrecht Verfasser aut Lectures on algebraic topology Albrecht Dold Reprint of the 1980 ed. Berlin u.a. Springer 1995 XI, 377 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Classics in mathematics Früher als: Grundlehren der mathematischen Wissenschaften ; 200 Weitere Ausgabe: Grundlehren der mathematischen Wissenschaften ; 200 Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 s DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006613642&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dold, Albrecht Lectures on algebraic topology Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4120861-4 |
| title | Lectures on algebraic topology |
| title_auth | Lectures on algebraic topology |
| title_exact_search | Lectures on algebraic topology |
| title_full | Lectures on algebraic topology Albrecht Dold |
| title_fullStr | Lectures on algebraic topology Albrecht Dold |
| title_full_unstemmed | Lectures on algebraic topology Albrecht Dold |
| title_short | Lectures on algebraic topology |
| title_sort | lectures on algebraic topology |
| topic | Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | Algebraic topology Algebraische Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006613642&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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