Algebraic Topology Summer term 2016 by Christoph Schweigert

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Algebraic Topology Summer term 2016 written by Christoph Schweigert, Hamburg University, Department of Mathematics, Section Algebra and Number Theory and Center for Mathematical Physics This is an other great mathematics book cover the following topics.

Homology theory
Chain complexes, Singular homology, The homology groups H0 and H1, Homotopy invariance, The long exact sequence in homology, The long exact sequence of a pair of spaces, Excision, Mayer-Vietoris sequence, Reduced homology and suspension, Mapping degree, CW complexes, Cellular homology, Homology with coefficients, Tensor products and the universal coefficient theorem, The topological K¨unneth formula

Singular cohomology
Definition of singular cohomology, Universal coefficient theorem for cohomology, Axiomatic description of a cohomology theory, Cap product, Cup product on cohomology, Orientability of manifolds, Cohomology with compact support, Poincar´e duality, Alexander-Lefschetz duality, Application of duality, Duality and cup products, The Milnor sequence, Lens spaces, A first quick glance on homotopy theory

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