Math 225C: Algebraic Topology
MWF 12 noon - 12:50pm,
Location: 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
E-mail: honda at math dot ucla dot
TA: Michael Miller; office hours
Th 1-3pm but "pretty much literally whenever"; smmiller
at ucla dot edu
- Homotopy theory: fundamental group,
covering spaces, Van Kampen's theorem.
- Homology theory: singular homology,
simplicial homology, homotopy invariance, relative
homology, excision and Mayer-Vietoris, functoriality,
relationship to the fundamental group, applications.
- Cohomology theory: singular
cohomology, cup products
Hatcher, Algebraic Topology,
Cambridge University Press. Also available for
free at author's website.
Greenberg and Harper, Algebraic
- Some knowledge of algebra and
There will be weekly problem sets; see
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!
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
Last modified: March 28, 2016.