Math 651 — Introductory Algebraic Topology

Spring 2003

Instructor: Jim West

Time: MWF 10:10-11:00

Room: MT 205

This will be a basic introductory course to the topic. We shall, in the main, follow Allen Hatcher's most excellent text Algebraic Topology (what else?). The core topics of this course are:

• Fundamental Group
• Covering Spaces
• Homology (both simplicial and singular).
• Polyhedra and CW-complexes (nice things to work with).

That is, roughly the first 2 chapters of Hatcher. There should be time for some applications, such as the Lefschetz Fixed Point Theorem, Brouwer's Fixed Point Theorem and Invariance of Domain Theorem, the nonexistence of a nowhere vanishing vector field on the 2-sphere, the Borsuk-Ulam Theorem, the Fundamental Theorem of Algebra, and others.