Acylindrical actions for two-dimensional Artin groups of hyperbolic type

2019/06/07 by Martin, Alexandre, Przytycki, Piotr · 1 citation
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1906.03154

Abstract

For a two-dimensional Artin group A whose associated Coxeter group is hyperbolic, we prove that the action of A on the hyperbolic space obtained by coning off certain subcomplexes of its modified Deligne complex is acylindrical. Moreover, if for each s∈ S there is t∈ S with m_st< ∞, then this action is universal. As a consequence, for |S|≥ 3, if A is irreducible, then it is acylindrically hyperbolic. We also obtain the Tits alternative for A, and we classify the subgroups of A that virtually split as a direct product. A key ingredient in our approach is a simple criterion to show the acylindricity of an action on a two-dimensional CAT(-1) complex.

Cited by

• Acylindrical Visual Splittings and The Tits Alternative For Artin Groups

Related

• Acylindrical hyperbolicity for Artin groups of dimension 2
• Acylindrical hyperbolicity of Artin groups associated with graphs that are not cones
• Acylindrical hyperbolicity from actions on CAT(0) cube complexes: a few criteria
• Acylindrically hyperbolic groups
• Acylindrical actions on CAT(0) square complexes