Math 225B: Differentiable Manifolds
MWF 2pm - 2:50pm,
Location: MS 5138
Discussion: Th 2pm - 2:50pm, Location: MS 5138
This is the second quarter of a year-long
sequence in geometry and topology.
Instructor: Ko Honda
Office: MS 7919
Office Hours: Wed 11am-noon, 1-1:50pm
E-mail: honda at math dot ucla dot
TA: Eilon Reisin-Tzur; office
hours TBA; ereisint at math
dot ucla dot edu
- Sard's theorem and transversality.
- Oriented intersection theory, degree,
Lefschetz fixed point theorem.
- Poincaré duality, Thom isomorphism,
- Hodge theory, elliptic operators
- Knowledge of basic manifold theory
(e.g., Math 225A)
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.
For the differential topology portion of the course:
For Poincaré duality and the Thom
- Guillemin & Pollack, Differential
- Milnor, Topology from the
For the Hodge theory portion of the course:
- Bott & Tu, Differential Forms
in Algebraic Topology.
Geometry Course Notes, second semester,
- Warner, Foundations of Differentiable Manifolds and
WARNING: The course syllabus provides a general
plan for the course; deviations may become
Last modified: January 2,