MA5236



Homology Theory

This module is designed for graduate students in mathematics. It covers the following major topics: Homological algebra: categories and functors, chain complexes, homology, exact sequences, Snake Lemma, Mayer-Vietoris, Kunneth Theorem. Homology theory: Eilenberg-Steenrod homology axioms, singular homology theory, cellular homology, cohomology, cup and cap products, applications of homology (Brouwer fixed-point theorem, vector fields on spheres, Jordan Curve Theorem), H-spaces and Hopf algebra. Manifolds: de Rham cohomology, orientation, Poincare duality.

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