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140122 ||| eng |
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|a 9783642678219
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| 100 |
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|a Dold, Albrecht
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| 245 |
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|a Lectures on Algebraic Topology
|h Elektronische Ressource
|c by Albrecht Dold
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| 250 |
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|a 2nd ed. 1995
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 1995, 1995
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| 300 |
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|a XI, 379 p
|b online resource
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|a §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 --
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|a §3 Extending Functors from Polyhedrons to More General Spaces
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|a 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 --
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|a §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 --
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| 653 |
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|a Algebraic Topology
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| 653 |
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|a Algebraic topology
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| 041 |
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|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Classics in Mathematics
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| 028 |
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|a 10.1007/978-3-642-67821-9
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| 856 |
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|u https://doi.org/10.1007/978-3-642-67821-9?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 514.2
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