Algebraic topology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2002
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XII, 544 Seiten Diagramme |
| ISBN: | 052179160X 0521795400 9780521791601 9780521795401 |
Staff View
MARC
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Record in the Search Index
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Table of Contents Preface . ix Standard Notations xii. Chapter 0. Some Underlying Geometric Notions . i Homotopy and Homotopy Type 1. Cell Complexes 5. Operations on Spaces 8. Two Criteria for Homotopy Equivalence 10. The Homotopy Extension Property 14. Chapter 1. The Fundamental Group. 1.1. Basic Constructions . 21 25 Paths and Homotopy 25. The Fundamental Group of the Circle 29. Induced Homomorphisms 34. 1.2. Van Kampen’s Theorem. 40 Free Products of Groups 41. The van Kämpen Theorem 43. Applications to Cell Complexes 50. 1.3. Covering Spaces. . . Lifting Properties 60. The Classification of Covering Spaces 63. Deck Transformations and Group Actions 70. Additional Topics l .A. Graphs and Free Groups 83. l.B. K(G,1) Spaces and Graphs of Groups 87. 56
Chapter 2. Homology. 97 2.1. Simplicial and Singular Homology. 102 A-Complexes 102. Simplicial Homology 104. Singular Homology 108. Homotopy Invariance 110. Exact Sequences and Excision 113. The Equivalence of Simplicial and Singular Homology 128. 2.2. Computations and Applications .134 Degree 134. Cellular Homology 137. Mayer-Vietoris Sequences 149. Homology with Coefficients 153. 2.3. The Formal Viewpoint.i60 Axioms for Homology 160. Categories and Functors 162. Additional Topics 2.A. Homology and Fundamental Group 166. 2.B. Classical Applications 169. 2.C. Simplicial Approximation 177. Chapter 3. Cohomology . iss 3.1. Cohomology Groups . 190 The Universal Coefficient Theorem 190. Cohomology of Spaces 197. 3.2. Cup Product . 206 The Cohomology Ring 212. A Künneth Formula 214. Spaces with Polynomial Cohomology 220. 3.3. Poincaré Duality. 230 Orientations and Homology 233. The Duality Theorem 239. Connection with Cup Product 249. Other Forms of Duality 252. Additional Topics 3.A. Universal Coefficients for Homology 261. 3.B. The General Künneth Formula 268. 3.C. Η-Spaces and Hopf Algebras 281. 3.D. The Cohomology of SO(n) 292. 3.E. Bockstein
Homomorphisms 303. 3.F. Limits and Ext 311. 3.G. Transfer Homomorphisms 321. 3.H. Local Coefficients 327.
Chapter 4. Homotopy Theory. 337 4.1. Homotopy Groups . 339 Definitions and Basic Constructions 340. Whitehead’s Theorem 346. Cellular Approximation 348. CW Approximation 352. 4.2. Elementary Methods of Calculation. 360 Excision for Homotopy Groups 360. The Hurewicz Theorem 366. Fiber Bundles 375. Stable Homotopy Groups 384. 4.3. Connections with Cohomology . зэз The Homotopy Construction of Cohomology 393. Fibrations 405. Postnikov Towers 410. Obstruction Theory 415. Additional Topics 4.A. Basepoints and Homotopy 421. 4.B. The Hopf Invariant 427. 4.C. Minimal Cell Structures 429. 4.D. Cohomology of Fiber Bundles 431. 4.E. The Brown Representability Theorem 448. 4.F. Spectra and Homology Theories 452. 4.G. Gluing Constructions 456. 4.H. Eckmann-Hilton Duality 460. 4.1. Stable Splittings of Spaces 466. 4.J. The Loopspace of a Suspension 470. 4.K. The Dold-Thom Theorem 475. 4.L. Steemod Squares and Powers 487. Appendix . 519 Topology of Cell Complexes 519. The Compact-Open Topology 529. Bibliography. 533 Index. 539 |
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| illustrated | Not Illustrated |
| indexdate | 2025-02-20T07:12:49Z |
| institution | BVB |
| isbn | 052179160X 0521795400 9780521791601 9780521795401 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009238197 |
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| physical | XII, 544 Seiten Diagramme |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Cambridge Univ. Press |
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| spellingShingle | Hatcher, Allen Algebraic topology 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_full | Algebraic topology Allen Hatcher |
| title_fullStr | Algebraic topology Allen Hatcher |
| title_full_unstemmed | Algebraic topology Allen Hatcher |
| title_short | Algebraic topology |
| title_sort | algebraic topology |
| topic | Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | Algebraic topology Algebraische Topologie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009238197&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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Indexes
Sonderstandort Fakultät
| Call Number: |
2000 SK 300 H361 |
|---|---|
| Copy 1 | nicht ausleihbar Checked out – Due: 31.12.2099 Recall This |