Stable cylinders and fine structures for hyperbolic groups and curve graphs

Harry Petyt; Davide Spriano; Abdul Zalloum

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arXiv · 2501.13600

Stable cylinders and fine structures for hyperbolic groups and curve graphs

Harry Petyt·Davide Spriano·Abdul Zalloum

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Abstract

In 1995, Rips and Sela asked if torsionfree hyperbolic groups admit globally stable cylinders. We establish this property for all residually finite hyperbolic groups and curve graphs of finite-type surfaces. These cylinders are fine objects, and the core of our approach is to upgrade the hyperbolic space to one with improved fine properties via a generalisation of Sageev's construction. The methods also let us prove that curve graphs of surfaces admit equivariant quasiisometric embeddings in finite products of quasitrees.

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Harry Petyt, Davide Spriano, Abdul Zalloum. 2025-01-23. Stable cylinders and fine structures for hyperbolic groups and curve graphs. https://arxiv.org/abs/2501.13600

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