Instructor: Ko Honda
Office: MS 7919
Office Hours: Mon 11-11:50am, Wed 2-2:50pm
E-mail: honda at math dot ucla dot edu
URL: http://www.math.ucla.edu/~honda

TA: Harahm Park; office hours Tu 4-5pm, Th 12-1pm;  harahmpark at math dot ucla dot edu

Class Meetings

• Lectures: MWF 12pm - 12:50pm, Location: MS 5203
• Discussion: Tu 12pm - 12:50pm, Location MS 5203
  

Topics

1. Differential forms: tensor and exterior algebra, exterior differentiation, and Lie derivatives.
2. Integration: Stokes' theorem, de Rham cohomology, and computations using Meyer-Vietoris sequences
3. Sard's theorem and transversality.
   
4. Oriented intersection theory, degree, Lefschetz fixed point theorem.
5. Poincaré duality, Thom isomorphism, Pontryagin-Thom theory

Prerequisites

• Knowledge of basic manifold theory (e.g., Math 225A)
  

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

1. Differential Geometry Course Notes
2. Lee, Introduction to Smooth Manifolds
   
3. Spivak, A Comprehensive Introduction to Differential Geometry
4. Tu, An Introduction to Manifolds
   
5. Warner, Foundations of Differentiable Manifolds and Lie Groups
6. Peter Petersen's notes

1. Guillemin & Pollack, Differential Topology,
2. Milnor, Topology from the Differentiable Viewpoint.
   

1. Bott & Tu, Differential Forms in Algebraic Topology.