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Surface groups are flexibly stable

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arxiv 1901.07182 v3 pith:CGKA7BAH submitted 2019-01-22 math.GR math.GT

Nir Lazarovich , Arie Levit , Yair Minsky This is my paper · ORCID
classification math.GRmath.GT
keywords flexiblygroupsstablesurfacealonganalysisbranchedcovers
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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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  1. Stability for product groups and property $(\tau)$

    math.GR 2019-08 accept novelty 8.0 of 10

    Product groups Σ×Λ are not very flexibly P-stable when Σ admits a non-abelian free quotient and Λ lacks property (τ), so P-stability is not closed under direct products.

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