CONCORDANCE CLASSES OF FREE ACTIONS OF COMPACT LIE GROUPS ON INFINITE DIMENSIONIAL MANIFOLDS

Abstract

This chapter presents the concordance classes of free actions of compact lie groups on infinite dimensional manifolds. Every free action of a compact Lie group G on a Q(l2)-manifold is G-concordant to a tame free action. Moreover, if the free action is tame on a Q(l2)-manifold, invariant Z-set N, then the concordance can be chosen to be relative to N. Consequently, every free n-toral action on Tn×Q is Tn-concordant to the trivial one. The chapter presents a theorem that states that given a compact Lie group G, every free G-action on a Q(l2)-manifold is G-concordant to a tame free action.