Acylindrical hyperbolicity of cubical small-cancellation groups

Goulnara N. Arzhantseva; Mark F. Hagen

Acylindrical hyperbolicity of cubical small-cancellation groups

Goulnara N. Arzhantseva, Mark F. Hagen

School of Mathematics

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Abstract

We provide an analogue of Strebel's classification of geodesic triangles in classical $C'(\frac16)$ groups for groups given by Wise's cubical presentations satisfying sufficiently strong metric cubical small-cancellation conditions. Using our classification, we prove that, except in specific degenerate cases, such groups are acylindrically hyperbolic.

Original language	English
Number of pages	37
Journal	Algebraic and Geometric Topology
Publication status	Published - 25 Oct 2022

Keywords

cubical small cancellation
acylindrically hyperbolic group

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title = "Acylindrical hyperbolicity of cubical small-cancellation groups",

abstract = "We provide an analogue of Strebel's classification of geodesic triangles in classical $C'(\frac16)$ groups for groups given by Wise's cubical presentations satisfying sufficiently strong metric cubical small-cancellation conditions. Using our classification, we prove that, except in specific degenerate cases, such groups are acylindrically hyperbolic.",

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AU - Arzhantseva, Goulnara N.

AU - Hagen, Mark F.

PY - 2022/10/25

Y1 - 2022/10/25

N2 - We provide an analogue of Strebel's classification of geodesic triangles in classical $C'(\frac16)$ groups for groups given by Wise's cubical presentations satisfying sufficiently strong metric cubical small-cancellation conditions. Using our classification, we prove that, except in specific degenerate cases, such groups are acylindrically hyperbolic.

AB - We provide an analogue of Strebel's classification of geodesic triangles in classical $C'(\frac16)$ groups for groups given by Wise's cubical presentations satisfying sufficiently strong metric cubical small-cancellation conditions. Using our classification, we prove that, except in specific degenerate cases, such groups are acylindrically hyperbolic.

KW - cubical small cancellation

KW - acylindrically hyperbolic group

M3 - Article (Academic Journal)

SN - 1472-2747

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

ER -

Acylindrical hyperbolicity of cubical small-cancellation groups

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