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arXiv · 2610.36211

Recognizing convergence actions as proper isometric actions on hyperbolic spaces

Lihuang Ding·Abdul Zalloum
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Abstract

Relying merely on B.I. (a.k.a. Bowditch's intelligence), we show that whenever a group $G$ admits a convergence action on a compact perfect metrizable space $M$, there is a hyperbolic space $X$ along with a proper isometric action of $G$ on $X$ inducing a $G$-equivariant homeomorphism $f:M \rightarrow \partial X.$ This answers a question by Misha Kapovich.

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Lihuang Ding, Abdul Zalloum. 2026-10-26. Recognizing convergence actions as proper isometric actions on hyperbolic spaces. https://arxiv.org/abs/2610.36211

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