The Lefschetz Fixed Point Theorem for Compact Groups

Abstract

It is shown that every compact group G is a Q-simplicial space where Q is any field of characteristic zero. As a consequence it follows that G satisfies a variation of the Lefschetz fixed point theorem. It has been known for some time that the Lefschetz fixed point theorem applies to a few spaces other than just ANR spaces, especially if some care is taken to use coefficients in certain fields [2]. The case of all compact groups provides a broad class of spaces which may not have local connectivity of any order. It is shown that every compact group G satisfies the Lefschetz fixed point theorem when coefficients for the homology groups are taken in a field of characteristic zero.