Cornell Math - MATH 753, Fall 2004

MATH 753: Algebraic Topology and Differential Forms (Fall 2004)

Instructor: Peter Kahn

Meeting Time & Room

This course develops many of the important concepts, techniques and results of algebraic topology from the viewpoint of differential forms, using material in the classical book of Bott and Tu. Topics will include de Rham's Theorem, Mayer-Vietoris theorems, Poincaré duality, some spectral-sequence theory, and some homotopy theory. If time permits, the course may include some of Warner's treatment of Hodge theory and/or a development of the theory of characteristic classes.

Prerequisites: Advanced calculus, linear algebra, and one semester of algebraic topology. It would be desirable to have some familiarity with differentiable manifolds and the basic objects used in connection with manifolds: tangent vectors, vector fields, differentiable forms, etc.