MATH 7321 — Topology 3

Course description Welcome to MATH 7321. This course is a continuation of Topology 2 (the Fundamental group, Homology and Cohomology) and introduces tools from homotopy theory such as homotopy groups and fibrations, as well as computational techniques like spectral sequences.

Syllabus: pdf

Topics:

  • Homotopy groups

  • Fibrations and fiber bundles

  • The theorems of Whitehead, Hurewicz and Freudenthal

  • Eilenberg-MacLane spaces and the representability of cohomology

  • Spectral sequences

Lectures:

  • Lecture 1 [01/09/2026] pdf: Course overview, homotopy groups