Math 227A:  Algebraic Topology

MWF 2-2:50pm
Location: MS 5148


This is a second course in algebraic topology.  After briefly reviewing the language of category theory and homological algebra, we discuss cohomology and homotopy theory, following Chapters 3 and 4 of Hatcher, Algebraic Topology.

Instructor: Ko Honda
Office: MS 7919
Office Hours: M 10-11:50am
honda at math dot ucla dot edu.

  1. Brief review of categorical language; some homological algebra
  2. Cohomology (universal coefficient theorem, cup products, Eilenberg-Zilber theorem, orientations, Poincaré duality)
  3. Homotopy theory (higher homotopy groups, Whitehead's theorem, cellular approximation theorem, CW approximations, excision, Hurewicz theorem, fibrations, stable homotopy groups, spectra, Brown representability, Steenrod operations)

  • Math 225C or equivalent (a good knowledge of Chapters 0-2 of Hatcher, Algebraic Topology)
  • Based on attendance.  If you want an A+, submit your stack of HW at the end of the quarter.
Hatcher, Algebraic Topology, Cambridge University Press.  Also available for free at author's website.

WARNING:  The course syllabus provides a general plan for the course; deviations may become necessary. 

Last modified: November 18, 2018