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Lieferstatus:	i.d.R. innert 7-14 Tagen versandfertig
Veröffentlichung:	Februar 1995
Genre:	Schulbücher
	Algebra / Algebraic Topology / B / boundary element method / cohomology / Homology / Mathematics / Mathematics and Statistics / Microsoft Access / Publishing / Topology mehr...
ISBN:	9783540586609
EAN-Code:	9783540586609
Verlag:	Springer
Einband:	Kartoniert
Sprache:	English
Dimensionen:	H 235 mm / B 155 mm / D
Gewicht:	715 gr
Seiten:	379
Illustration:	XI, 379 p.
Zus. Info:	EUDR exemption - product or manufacturing materials placed on the market prior to 31.12.2025.
Bewertung:	Titel bewerten / Meinung schreiben

Inhalt:

I Preliminaries on Categories, Abelian Groups, and Homotopy.- ?Categories and Functors.- ?Abelian Groups (Exactness, Direct Sums, Free Abelian Groups).- ?Homotopy.- II Homology of Complexes.- ?Complexes.- ?Connecting Homomorphism, Exact Homology Sequence.- ?Chain-Homotopy.- ?Free Complexes.- III Singular Homology.- ?Standard Simplices and Their Linear Maps.- ?The Singular Complex.- ?Singular Homology.- ?Special Cases.- ?Invariance under Homotopy.- ?Barycentric Subdivision.- ?Small Simplices. Excision.- ?Mayer-Vietoris Sequences.- IV Applications to Euclidean Space.- ?Standard Maps between Cells and Spheres.- ?Homology of Cells and Spheres.- ?Local Homology.- ?The Degree of a Map.- ?Local Degrees.- ?Homology Properties of Neighborhood Retracts in ?n.- ?Jordan Theorem, Invariance of Domain.- ?Euclidean Neighborhood Retracts (ENRs).- V Cellular Decomposition and Cellular Homology.- ?Cellular Spaces.- ?CW-Spaces.- ?Examples.- ?HomologyProperties of CW-Spaces.- ?The Euler-Poincar? Characteristic.- ?Description of Cellular Chain Maps and of the Cellular Boundary Homomorphism.- ?Simplicial Spaces.- ?Simplicial Homology.- VI Functors of Complexes.- ?Modules.- ?Additive Functors.- ?Derived Functors.- ?Universal Coefficient Formula.- ?Tensor and Torsion Products.- ?Horn and Ext.- ?Singular Homology and Cohomology with General Coefficient Groups.- ?Tensorproduct and Bilinearity.- ?Tensorproduct of Complexes. K?neth Formula.- ? Horn of Complexes. Homotopy Classification of Chain Maps.- ? Acyclic Models.- ? The Eilenberg-Zilber Theorem. Kunneth Formulas for Spaces.- VII Products.- ?The Scalar Product.- ?The Exterior Homology Product.- ? 3 The Interior Homology Product (Pontijagin Product).- ? 4 Intersection Numbers in ?n.- ?The Fixed Point Index.- ?The Lefschetz-Hopf Fixed Point Theorem.- ?The Exterior Cohomology Product.- ? 8 The Interior Cohomology Product (?-Product).- ? 9 ?-Products in Projective Spaces. Hopf Maps and Hopf Invariant.- ? Hopf Algebras.- ? The Cohomology Slant Product.- ? The Cap-Product (?-Product).- ? 13 The Homology Slant Product, and the Pontijagin Slant Product.- VIII Manifolds.- ?Elementary Properties of Manifolds.- ?The Orientation Bundle of a Manifold.- ?Homology of Dimensions ? n in n-Manifolds.- ?Fundamental Class and Degree.- ?Limits.- ??ech Cohomology of Locally Compact Subsets of ?n.- ?Poincar?-Lefschetz Duality.- ?Examples, Applications.- ?Duality in ?-Manifolds.- ? Transfer.- ? Thom Class, Thom Isomorphism.- ? The Gysin Sequence. Examples.- ? Intersection of Homology Classes.- Appendix: Kan- and ?ech-Extensions of Functors.- ?Limits of Functors.- ?Polyhedrons under a Space, and Partitions of Unity.- ?Extending Functors from Polyhedrons to More General Spaces.