Algebraic topology II 1000-135TA2
Homological algebra in the category of abelian groups (Z-modules). Homology and cohomology theories. Axioms of Eilenberg and Steenrod. Homology and cohomology theory of CW-complexes. Mayer-Vietoris sequences. Relation between homotopy and homology: Hurewicz theorem. Cohomology of a space as an algebra. Homology theory of closed manifolds - duality theorems. Applications of algebraic methods in topology, for example: Lefschetz's fixed-point theorem, generalized Jordan's theorem, applications of duality theorems.
Type of course
Prerequisites
Bibliography
R. Bott, L.W. Tu, Differential Forms in Algebraic Topology. Graduate Texts in Mathematics 82, Springer Verlag, New York 1982
G. Bredon, Topology and Geometry, Graduate Texts in Mathematics 139, Springer Verlag, New York 1993
M. Aguilar, S. Gitler, C. Prieto, Algebraic Topology from a Homotopical Viewpoint. Universitext, Springer Verlag, New York 2002
A. Hatcher, Algebraic Topology, Cambridge University Press, Cambridge 2002 (accessible in the web)
P. May, A Concise Course in Algebraic Topology. Chicago Lecture Notes in Mathematics, The University of Chicago and London, 1999
E. Spanier, Algebraic Topology
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