Homotopy Fixed-point Methods for Lie Groups and Finite Loop Spaces

Abstract

A loop space X is by definition a triple (X, BX, e) in which X is a space, BX is a connected pointed space, and e: X -QBX is a homotopy equivalence from X to the space QBX of based loops in BX. We will say that a loop space X is finite if the integral homology H*(X, Z) is finitely generated as a graded abelian group, i.e., if X appears at least homologically to be a finite complex. In this paper we prove the following theorem.