Stable cylinders and fine structures for hyperbolic groups and curve graphs

Fuente: arXiv
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Main Authors: Petyt, Harry, Spriano, Davide, Zalloum, Abdul
Format: Preprint
Published: 2025
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author Petyt, Harry
Spriano, Davide
Zalloum, Abdul
author_facet Petyt, Harry
Spriano, Davide
Zalloum, Abdul
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2501_13600
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Stable cylinders and fine structures for hyperbolic groups and curve graphs
Petyt, Harry
Spriano, Davide
Zalloum, Abdul
Geometric Topology
Group Theory
Metric Geometry
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.
title Stable cylinders and fine structures for hyperbolic groups and curve graphs
topic Geometric Topology
Group Theory
Metric Geometry
url https://arxiv.org/abs/2501.13600