On acylindrical hyperbolicity of groups with positive first $\ell^2$-Betti number

D. Osin

doi:10.1112/blms/bdv047

On acylindrical hyperbolicity of groups with positive first $\ell^2$-Betti number

Group Theory 2018-05-16 v2 Geometric Topology Operator Algebras

Authors: D. Osin

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Abstract

We prove that every finitely presented group with positive first $\ell^2$ -Betti number that virtually surjects onto $\mathbb Z$ is acylindrically hyperbolic. In particular, this implies acylindrical hyperbolicity of finitely presented residually finite groups with positive first $\ell^2$ -Betti number as well as groups of deficiency at least $2$ .

Keywords

acylindrically hyperbolic groups finitely presented groups l2-Betti numbers residually finite groups group deficiency virtual surjection

Cite

@article{arxiv.1501.03066,
  title  = {On acylindrical hyperbolicity of groups with positive first $\ell^2$-Betti number},
  author = {D. Osin},
  journal= {arXiv preprint arXiv:1501.03066},
  year   = {2018}
}

Comments

The published version of this paper used a result from arXiv:1310.6289 whose proof contained a gap. The gap and necessary changes to the published version of this paper are discussed in arXiv:1711.09486. This version incorporates these changes

On acylindrical hyperbolicity of groups with positive first $\ell^2$-Betti number

Abstract

Keywords

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