Localization and Donaldson-Witten Theory - A Quick Survey

Here I will try to describe the motivation behind the lecture series by discussing, quite informally, Cartan's generalization of the Chern-Weil construction of characteristic classes in equivariant cohomology, the Mathai-Quillen repesentatives of the Thom and Euler classes, the phenomenon of localization and a formal extension of these finite-dimensional theorems by Atiyah-Jeffrey to an infinite-dimensional context related to the Donaldson invariants and Witten'S (1988) topoloigical quantum field theory. The remaining lectures will provide a few more detials on the localization theorems.