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arXiv · 2504.18811

A characterization of proper actions with bornology and coarse geometry

Hiroaki Nagaya
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Abstract

In 1961, Palais showed that every smooth proper Lie group action on a smooth manifold admits a compatible 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 compatible uniform structure making the action equi continuous in an appropriate setting. In this paper, we focus on bornological proper actions on bornological spaces and prove that the space admits a compatible coarse structure such that the action becomes equi controlled.

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Hiroaki Nagaya. 2025-04-26. A characterization of proper actions with bornology and coarse geometry. https://arxiv.org/abs/2504.18811

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