Algebraic characterisation of relatively hyperbolic special groups

2017/09/05 by Genevois, Anthony · 1 citation
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1709.01258

Abstract

This article is dedicated to the characterisation of the relative hyperbolicity of Haglund and Wise's special groups. More precise, we introduce a new combinatorial formalism to study (virtually) special groups, and we prove that, given a cocompact special group G and a finite collection of subgroups H, then G is hyperbolic relative to H if and only if (i) each subgroup of H is convex-cocompact, (ii) H is an almost malnormal collection, and (iii) every non-virtually cyclic abelian subgroup of G is contained in a conjugate of some group of H. As an application, we show that a virtually cocompact special group is hyperbolic relative to abelian subgroups if and only if it does not contain \mathbbF₂ × ℤ.

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• Strong solidity classification of Coxeter groups

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