Cornell Math - MATH 651, Spring 2004

MATH 651: Introduction to Algebraic Topology (Spring 2004)

Instructor: James West

Meeting Time & Room

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 knot groups and the Alexander polynomial, the Lefschetz Fixed Point Theorem, Brouwer's Fixed Point Theorem and Invariance of Domain Theorem, the nonexistence of a nowhere zero vector field on the 2-sphere, the Borsuk-Ulam Theorem, the Fundamental Theorem of Algebra, and/or others, depending on interest.