**Math 225B: Differentiable Manifolds**
## Winter 2020
Lectures:*
*MWF 2pm - 2:50pm,
Location: MS 5138
Discussion: Th 2pm - 2:50pm, Location: MS 5138
*Syllabus*
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
edu
**URL: ***http://www.math.ucla.edu/~honda*
**TA: **Eilon Reisin-Tzur; office
hours TBA; *ereisint** at** **math
dot ucla dot edu*
**Topics**
- Sard's theorem and transversality.
- Oriented intersection theory, degree,
Lefschetz fixed point theorem.
- Poincaré duality, Thom isomorphism,
Pontryagin-Thom theory
- Hodge theory, elliptic operators
**Prerequisites**
- Knowledge of basic manifold theory
(e.g., Math 225A)
**Homework**
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.
**References**
For the differential topology portion of the course:
- Guillemin & Pollack,
*Differential
Topology,*
- Milnor,
*Topology from** the
Differentia**ble Viewpoint.*
For Poincaré duality and the Thom
isomorphism:
- Bott & Tu,
*Differential **Forms
in Algebraic Topology.*
For the Hodge theory portion of the course:
- Differential
Geometry Course Notes, second semester,
- Warner, Foundations of Differentiable Manifolds and
Lie Groups.
WARNING: The course syllabus provides a general
plan for the course; deviations may become
necessary.
Last modified: January 2,
2020. |