Countable approximation of topological $G$-manifolds: compact Lie groups $G$

Abstract

Let $G$ be a compact Lie group. (Compact) topological $G$-manifolds have the $G$-homotopy type of (finite-dimensional) countable $G$-CW complexes (2.5). This partly generalizes Elfving's theorem for locally linear $G$-manifolds [Elf96], wherein the Lie group $G$ is linear (such as compact).

8 pages. Version 3: improved historical scholarship (inserted 2.3, 3.3, 4.4; generalized 4.3). accepted for publication

References in corpus (1)

• Topological rigidity and actions on contractible manifolds with discrete singular set

Cited by in corpus (1)

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