Math 753 — Fall 2001 Algebraic Topology

This is a second semester course in algebraic topology, the sequel to the introductory course, Math 651. The main topics will be cohomology and homotopy groups. In particular the course will cover: universal coefficient theorems, cup products, Kunneth formulas, Poincaré duality, the Hurewicz theorem, the Freudenthal suspension theorem, fiber bundles, fibrations, and Postnikov towers. If time permits there may also be a brief introduction to the Serre spectral sequence.

Textbook: Chapters 3 and 4 of my algebraic topology book.