Countable approximation of topological G-manifolds, II: linear Lie groups G

Abstract

Let [Formula: see text] be a matrix group. Topological [Formula: see text]-manifolds with Palais-proper action have the [Formula: see text]-homotopy type of countable [Formula: see text]-CW complexes (3.2). This generalizes Elfving’s dissertation theorem for locally linear [Formula: see text]-manifolds (1996). Also, we improve the Bredon–Floyd theorem from compact Lie groups [Formula: see text] to arbitrary Lie groups [Formula: see text].