MATH 6510: Algebraic Topology I (Spring 2011)

Instructor: Allen Hatcher

This is the introductory course in algebraic topology. The principal focus is on methods for associating algebraic objects, mainly groups, to topological spaces. The simplest of these is the fundamental group of a space, with its associated theory of covering spaces. After this come the homology groups of a space. Developing the machinery of algebraic topology takes a fair amount of time, but once the machinery is available there are many quick pay-offs. In the course we will try to save some time by omitting details of longer proofs in class since these are readily available in textbooks. This should allow us to at least introduce some later topics such as higher homotopy groups and cohomology groups.

The official textbook for the course will be my book Algebraic Topology, freely available online. Prerequisites for the course are a basic understanding of point-set topology and abstract algebra (mostly group theory) at the undergraduate level.