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＜電子ブック＞
Lectures on Algebraic Topology / by Albrecht Dold
(Classics in Mathematics. ISSN:25125257)

版	2nd ed. 1995.
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
冊子体	Lectures on algebraic topology / Albrecht Dold.
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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-3-642-67821-9

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