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Lectures on Algebraic Topology / by Albrecht Dold
(Classics in Mathematics. ISSN:25125257)
版 | 2nd ed. 1995. |
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出版者 | (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer) |
出版年 | 1995 |
本文言語 | 英語 |
大きさ | XI, 379 p : online resource |
著者標目 | *Dold, Albrecht author SpringerLink (Online service) |
件 名 | LCSH:Algebraic topology FREE:Algebraic Topology |
一般注記 | I Preliminaries on Categories, Abelian Groups, and Homotopy -- §1 Categories and Functors -- §2 Abelian Groups (Exactness, Direct Sums, Free Abelian Groups) -- §3 Homotopy -- II Homology of Complexes -- §1 Complexes -- §2 Connecting Homomorphism, Exact Homology Sequence -- §3 Chain-Homotopy -- §4 Free Complexes -- III 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 -- IV 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 ?n -- §7 Jordan Theorem, Invariance of Domain -- §8 Euclidean Neighborhood Retracts (ENRs) -- V Cellular Decomposition and Cellular Homology -- §1 Cellular Spaces -- §2 CW-Spaces -- §3 Examples -- §4 HomologyProperties of CW-Spaces -- §5 The Euler-Poincaré Characteristic -- §6 Description of Cellular Chain Maps and of the Cellular Boundary Homomorphism -- §7 Simplicial Spaces -- §8 Simplicial Homology -- VI Functors of Complexes -- §1 Modules -- §2 Additive Functors -- §3 Derived Functors -- §4 Universal Coefficient Formula -- §5 Tensor and Torsion Products -- §6 Horn and Ext -- §7 Singular Homology and Cohomology with General Coefficient Groups -- §8 Tensorproduct and Bilinearity -- §9 Tensorproduct of Complexes. Künneth Formula -- §10 Horn of Complexes. Homotopy Classification of Chain Maps -- §11 Acyclic Models -- §12 The Eilenberg-Zilber Theorem. Kunneth Formulas for Spaces -- VII Products -- §1 The Scalar Product -- §2 The Exterior Homology Product -- § 3 The Interior Homology Product (Pontijagin Product) -- § 4 Intersection Numbers in ?n -- §5 The Fixed Point Index -- §6 The Lefschetz-Hopf Fixed Point Theorem -- §7 The Exterior Cohomology Product -- § 8 The Interior Cohomology Product (?-Product) -- § 9 ?-Products in Projective Spaces. Hopf Maps and Hopf Invariant -- §10 Hopf Algebras -- §11 The Cohomology Slant Product -- §12 The Cap-Product (?-Product) -- § 13 The Homology Slant Product, and the Pontijagin Slant Product -- VIII Manifolds -- §1 Elementary Properties of Manifolds -- §2 The Orientation Bundle of a Manifold -- §3 Homology of Dimensions ? n in n-Manifolds -- §4 Fundamental Class and Degree -- §5 Limits -- §6 ?ech Cohomology of Locally Compact Subsets of ?n -- §7 Poincaré-Lefschetz Duality -- §8 Examples, Applications -- §9 Duality in ?-Manifolds -- §10 Transfer -- §11 Thom Class, Thom Isomorphism -- §12 The Gysin Sequence. Examples -- §13 Intersection of Homology Classes -- Appendix: Kan- and ?ech-Extensions of Functors -- §1 Limits of Functors -- §2 Polyhedrons under a Space, and Partitions of Unity -- §3 Extending Functors from Polyhedrons to More General Spaces HTTP:URL=https://doi.org/10.1007/978-3-642-67821-9 |
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Springer eBooks | 9783642678219 |
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EB00231378 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA612-612.8 DC23:514.2 |
書誌ID | 4000110232 |
ISBN | 9783642678219 |
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