Surface groups are flexibly stable

Nir Lazarovich; Arie Levit; Yair Minsky

doi:10.4171/JEMS/1406

Surface groups are flexibly stable

Nir Lazarovich, Arie Levit, Yair Minsky

Technion - Israel Institute of Technology, Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We show that surface groups are flexibly stable in permutations. This is the first nontrivial example of a non-amenable flexibly stable group. Our method is purely geometric and relies on an analysis of branched covers of hyperbolic surfaces. Along the way we establish a quantitative variant of the LERF property for surface groups which may be of independent interest.

Original language	English
Pages (from-to)	1739-1768
Number of pages	30
Journal	Journal of the European Mathematical Society
Volume	27
Issue number	4
DOIs	https://doi.org/10.4171/JEMS/1406
State	Published - 2025

Keywords

CAT.‒1/
LERF
Stability in permutations
combinatorial group theory
flexible stability
surface groups

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.4171/JEMS/1406

Cite this

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title = "Surface groups are flexibly stable",

abstract = "We show that surface groups are flexibly stable in permutations. This is the first nontrivial example of a non-amenable flexibly stable group. Our method is purely geometric and relies on an analysis of branched covers of hyperbolic surfaces. Along the way we establish a quantitative variant of the LERF property for surface groups which may be of independent interest.",

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AB - We show that surface groups are flexibly stable in permutations. This is the first nontrivial example of a non-amenable flexibly stable group. Our method is purely geometric and relies on an analysis of branched covers of hyperbolic surfaces. Along the way we establish a quantitative variant of the LERF property for surface groups which may be of independent interest.

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KW - Stability in permutations

KW - combinatorial group theory

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KW - surface groups

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DO - 10.4171/JEMS/1406

M3 - مقالة

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SP - 1739

EP - 1768

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

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Surface groups are flexibly stable

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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