Abstract

In this article, we will study the equivariant cohomology theory for actions of compact group (not necessarily Lie group) on compact spaces. We will present a somewhat more general and shorter proof of the localization theorem, known as the Borel-Hsiang-Quillen localization theorem, which was generalized by Özkurt and Onat to actions of finite-dimensional compact groups on compact connected spaces. In particular, we will apply this to the problem of the existence of equivariant maps between topological transformation groups.

Keywords: Equivariant cohomology; Borel-Hsiang-Quillen localization theorem; Borsuk-Ulam type theorem.

MSC: 55N25, 54H15, 55N91, 22C05

DOI: 10.57016/MV-WXBY1959

Pages:  1--9