JournalsjemsVol. 27, No. 4pp. 1739–1768

Surface groups are flexibly stable

  • Nir Lazarovich

    Technion–Israel Institute of Technology, Haifa, Israel

  • Arie Levit

    Tel Aviv University, Israel

  • Yair Minsky

    Yale University, New Haven, USA
Surface groups are flexibly stable cover
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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.

Cite this article

Nir Lazarovich, Arie Levit, Yair Minsky, Surface groups are flexibly stable. J. Eur. Math. Soc. 27 (2025), no. 4, pp. 1739–1768

DOI 10.4171/JEMS/1406