Algebraic Topology 2

Algebraic Topology 2-Course outline

This course is a continuation of Algebraic Topology 1. In Algebraic Topology 2, we will cover the following material:

1. A review of singular homology and a study of other homology theories: simplicial complexes and cell complexes, simplicial homology and cellular homology, comparison theorems.

2. Cohomology: definition of singular cohomology, ring structure, functoriality, Mayer-Vietoris and excision, Künneth formula.

3. Topological manifolds and Poincare duality, universal coefficient theorems

4. Other topics as time permits: Steenrod operation, higher homotopy groups and homotopy theory, differentiable manifolds, differential forms, Stokes' theorem and the de Rham theorem.

The text is: A. Hatcher, Algebraic topology. Cambridge University Press, Cambridge, 2002.

As in Algebraic topology 1, there will be homework assignments, roughly one per week, and an exam at the end of the course (possibly oral exams). The course will be taught by:

Dr. Guissepe Ancona, Dr. Oleg Pokopaev and Dr. Bradley Drew.

There will be an organizational meeting on Tues. October 15, 12 noon, in WSC-O-3.46, to set the meeting times.