Math 225C:  Algebraic Topology

Spring 2016

Lectures: MWF 12 noon - 12:50pmLocation: MS 5148
Discussion: Th 12 noon - 12:50pm, Location: MS 7608


This is the third quarter of a year-long sequence in geometry and topology.

Instructor: Ko Honda
Office: MS 7901
Office Hours: Mon 11-12 noon
honda at math dot ucla dot edu.
Telephone: 310-825-2143

TA: Michael Miller; office hours Th 1-3pm but "pretty much literally whenever"; smmiller at ucla dot edu


  1. Homotopy theory: fundamental group, covering spaces, Van Kampen's theorem.
  2. Homology theory: singular homology, simplicial homology, homotopy invariance, relative homology, excision and Mayer-Vietoris, functoriality, relationship to the fundamental group, applications.
  3. Cohomology theory: singular cohomology, cup products


    Hatcher, Algebraic Topology, Cambridge University Press.  Also available for free at author's website.

Other references

    Greenberg and Harper, Algebraic Topology.


  • Some knowledge of algebra and point-set topology.

There will be weekly problem sets; see the class schedule.  Homework is due on Mondays, although there may be some exceptional weeks.  The problem sets count for a large percentage of your total grade (approximately 70%).  You may work with others or consult other textbooks, but the homework you turn in must be written by you, in your own words, and you must cite your sources used and your collaborators!

Final examination

There will be a take-home final.  This will be approximately 30% of your final grade.

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

Last modified: March 28, 2016.