Algebraic Topology


Algebraic topology aims to capture essential features of topological spaces in terms of algebraic objects like groups and rings.

This course can be considered as a continuation of the "Introduction to Algebraic Topology" (Math 232) course, but can be taken independently as well. The only formal prerequisites are basic algebra, point-set topology, and the notion of the fundamental group of a topological space.

Topics shall include:

Homology: A review of simplicial homology, Singular homology, Excision, Mayer-Vietoris theorem, CW-complexes and Cellular homology, Classical Applications including the Jordan Curve Theorem.

Cohomology: Cohomology groups, Universal coefficient theorems, Cup products, Kunneth formula, Orientation on manifolds, Poincare duality, introduction to smooth manifolds and de Rham cohomology.

Course description

Check for updates at the announcements and homework pages.