Mathematics 262, Fall 2008

Algebraic Topology II

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 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