Math 227A:  Algebraic Topology

MWF 2-2:50pm
Location: MS 5148

Syllabus

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
E-mail: honda at math dot ucla dot edu.
URL: http://www.math.ucla.edu/~honda

Topics
  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)

Prerequisites
  • Math 225C or equivalent (a good knowledge of Chapters 0-2 of Hatcher, Algebraic Topology)
Grading
  • Based on attendance.  If you want an A+, submit your stack of HW at the end of the quarter.
Textbook
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