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arXiv · 1901.07182

Surface groups are flexibly stable

Nir Lazarovich·Arie Levit·Yair Minsky
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Abstract

We show that surface groups are flexibly stable in permutations. This is the first non-trivial 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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Nir Lazarovich, Arie Levit, Yair Minsky. 2025-01-09. Surface groups are flexibly stable. https://doi.org/10.4171/jems%2F1406

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