On the homotopy fixed point problem for free loop spaces and other function complexes (original) (raw)
Let G be a finite group, let X and Y be finite G-complexes, and suppose that for each K ___ G, yK is dim(X x)-connected and simple. G acts on the function complex F(X, Y) by conjugation of maps. We give a complete analysis of the homotopy fixed point set of the space 92~E~ Y). As a corollary, we are able to analyze at a prime p, the homotopy fixed point set of the circle action on f~E~AX, where AX denotes the free loop space of X, and X is a simply connected finite complex.
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