INTRODUCTION TO ALGEBRAIC TOPOLOGY

Fundamental Group: Homotopy of maps, The fundamental group, Fundamental group of the circle, Covering spaces, Borsuk-Ulam and Ham-sandwich theorems, A lifting criterion, Seifert-van kampen theorem, Brouwer fixed point theorem and other applications.

Piecewise-Linear Topology: Polyhedra, PL maps, PL manifolds, Cell complexes, Subdivisions, Simplicial complexes, Simplicial maps, Triangulations, Derived subdivisions, Pseudomanifolds, Abstract simplicial complexes, isomorphism.

Simplicial Homology: Orientation of complexes, Chains, Cycles and boundaries, Homology groups, Euler-Poincare formula, Barycentric subdivision, Simplicial approximation, Induced homomorphism, Degree and Lefschetz number fixed-point theorem.  

Books


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Last updated: 20 May 2024