A characterization of proper actions with bornology and coarse geometry
Abstract
In 1961, Palais showed that every smooth proper Lie group action on a smooth manifold admits a Riemannian metric on the manifold such that the action becomes isometric. In 2006, Yoshino studied a continuous proper action of a locally compact Hausdorff group on a locally compact Hausdorff space, and showed that the space carries a uniform structure making the action equi-continuous in an appropriate setting. In this paper, we focus on bornologically proper actions on bornological spaces and prove that the space admits a coarse structure such that the action becomes equi-controlled.
Fields of Study & Subjects
Advanced Operator Algebra Research
Homotopy and Cohomology in Algebraic Topology
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- International Journal of Mathematics
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 37
- Issue
- 09
- Publication date
- 9 April 2026
- Language
- EN