Circle action, lower bound of fixed points and characteristic numbers

Abstract

Given an $S^1$-manifold with isolated fixed points, some recent papers are concerned with the relationship between the least number of fixed points and the characteristic numbers of this manifold, and their proofs have some similar features. The main purpose of this short survey article is, by using the language of equivariant cohomology, to present a unified method to deal with such problems, of which the related known results are direct corollaries.