Instructor: Shuguang Wang

Description: This is a continuation course of Math 8250 (Basic Topology and Geometry). Prerequisite is minimum: only Math 8250 is required. The main topics include Transversality, Degree of maps, Sard Theorem, and basic Morse Theory if time permits. These materials have had various applications in Dynamical Systems, Economics (Topology of Market) etc, in additional to being the foundation of further current research in the field of Topology.

Textbook: The primary textbook is M.W. Hirsch: Differential Topology, Springer, 1976.
Supplementary reading includes V. Guillemin and A. Pollack: Differential Topology, Prentice-Hall, 1974.