Math 227A: Algebraic
TopologyMWF 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, Instructor: Ko Honda Office: MS 7919Office Hours: M 10-11:50amE-mail: honda at math dot ucla dot
edu.URL: http://www.math.ucla.edu/~honda
Topics- Brief review of categorical language; some homological algebra
- Cohomology (universal coefficient theorem, cup
products, Eilenberg-Zilber theorem, orientations,
PoincarĂ© duality)
- 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,
*Al**gebraic Topology*)
Grading
- Based on attendance. If you want
an A+, submit your stack of HW at the end of the
quarter.
Textbook
Hatcher, WARNING: The course syllabus provides a general plan for the course; deviations may become necessary. Last modified: November 18, 2018 |