Titlebook: Algebraic Topology - Homotopy and Homology; Robert M. Switzer Book 2002 Springer-Verlag GmbH Germany 2002 Algebraic topology.YellowSale200

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-Complexes,ological spaces. One of the difficulties is that given two arbitrary topological spaces . it is very difficult to construct any map .: . → .. If we restricted our attention to a class of spaces built up step by step out of simple building blocks (think of simplicial complexes, for example), then we

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Homotopy Properties of ,-Complexes,will be consequences of the simplicial approximation theorem. In addition, we shall show that if .: . → . is a map between .-complexes such that .: .(., .) → .(., .) is an isomorphism for all . ⩾ 0, then. is a homotopy equivalence.

tympanometry

finite

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Representation Theorems,shall prove a converse result: given a cohomology theory . satisfying the wedge axiom on .’ we shall construct a spectrum . and a natural equivalence of cohomology theories .: .* →p .* on .’. In fact, we shall do somewhat more than that; for any cofunctor .*: .’ → . satisfying the wedge axiom and a

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Ordinary Homology Theory,ingular homology . is an ordinary homology theory with coefficients . on the category .’. We shall show that any two ordinary homology theories with coefficients . satisfying the wedge and WHE axioms are naturally equivalent. We shall also construct the Eilenberg-MacLane spectrum . with

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Vector Bundles and ,-Theory,ose for which every fibre has the structure of a vector space in a way which is compatible on neighboring fibres. We show how equivalence classes of such vector bundles over a .-complex can be used to define groups .*(.) in such a way that .* becomes a cohomology theory.

laceration

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Products,homology functors: one wants to investigate the existence or nonexistence of maps .: . → . by looking at the corresponding algebraic morphisms .:.(.) → .(.). As we have said before, the richer the algebraic structure on .(.), the more useful . will be for these investigations. In this chapter we int

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