Instructor: Lenny Ng

E-mail: ng AT math.duke.edu

Office: Physics 231

Office phone: 919-660-6972

Office hours: TTh 9:45-11:00 am

Course meeting time and place: TTh 8:30-9:45 am, Physics 205

Textbook: *Differential Forms in Algebraic Topology*,
by R. Bott and L. Tu. Other texts that will be useful
are *Algebraic Topology* by A. Hatcher and
possibly *Characteristic Classes* by J. Milnor and J. Stasheff.

There will be **no class** on the following days: September 16,
September 18, October 9. Classes will run through December 4 with a
possibility of a make-up class some time during the semester.

Homework assignments:

- Homework 1, due September 25
- Homework 2, due October 16
- Homework 3, due October 30
- Homework 4, due December 2

Here are topics that I plan to cover in the course. Topics near the end of this list are probably wishful thinking.

- Singular cohomology, cup product, Poincaré duality
- Differential forms, de Rham cohomology, Poincaré duality (again), Künneth Theorem
- Vector bundles, Thom isomorphism
- Cech cohomology, presheaves
- Spectral sequences, equivalence of cohomology theories, Leray-Serre spectral sequence
- Homotopy groups of spheres, long exact sequence for fiber bundles
- Characteristic classes of vector bundles