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Preprint Number 1784

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1784. Simon André
Acylindrical hyperbolicity and existential closeness

Submission date: 14 May 2020


Let G be a finitely presented group, and let H be a subgroup of G. We prove that if H is acylindrically hyperbolic and existentially closed in G, then G is acylindrically hyperbolic. As a corollary, any finitely presented group which is existentially equivalent to the mapping class group of a surface of finite type, to Out(F_n) or Aut(F_n) for n ≥ 2 or to the Higman group, is acylindrically hyperbolic.

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Full text arXiv 2005.07220: pdf, ps.

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