Proper actions and proper invariant metrics

Herbert Abels; Antonios Manoussos; Gennady Noskov

doi:10.1112/jlms/jdq091

Proper actions and proper invariant metrics

Metric Geometry 2014-02-26 v2 General Topology

Authors: Herbert Abels , Antonios Manoussos , Gennady Noskov

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

We show that if a (locally compact) group $G$ acts properly on a locally compact $\sigma$ -compact space $X$ then there is a family of $G$ -invariant proper continuous finite-valued pseudometrics which induces the topology of $X$ . If $X$ is furthermore metrizable then $G$ acts properly on $X$ if and only if there exists a $G$ -invariant proper compatible metric on $X$ .

Keywords

group actions algebraic group actions topological groups

Cite

@article{arxiv.math/0702322,
  title  = {Proper actions and proper invariant metrics},
  author = {Herbert Abels and Antonios Manoussos and Gennady Noskov},
  journal= {arXiv preprint arXiv:math/0702322},
  year   = {2014}
}

Comments

The paper has been completely rewritten and differs essentially from "Constructing invariant Heine-Borel metrics for proper G-spaces". The main result extended to the more general case when $G$ is a topological group which acts properly on a locally compact $\sigma$-compact Hausdorff space $X$. Note that there is a gap in the proof of Theorem 2.4 of the old version

Proper actions and proper invariant metrics

Abstract

Keywords

Cite

Comments

Related papers