MANIFOLDS MODELED BY AN EQUIVARIANT HILBERT CUBE

Abstract

J. E. West posed the general problem of carrying over the basics of the theory of manifolds modeled by the Hilbert cube ( -manifolds) into the equivariant realm. In particular, under the number 942 in “Open problems in topology” he formulated the following problem: “If is a locally compact G-CW complex, is the diagonal -action on a -manifold? [ is a compact Lie group and is the product of the unit balls of all the irreducible real representations of , each representation disc being represented infinitely often.] What if is a locally compact -ANR?” In this paper we construct a theory of -manifolds for an arbitrary compact group in a scope that suffices for proving a characterization theorem for such manifolds. Bibliography: 17 titles.