# Relative Cubulation of Small Cancellation Free Products

@inproceedings{Einstein2021RelativeCO, title={Relative Cubulation of Small Cancellation Free Products}, author={Eduard Einstein and Thomas Ng}, year={2021} }

We expand the class of groups with relatively geometric actions on CAT(0) cube complexes by proving that it is closed under C′( 1 6 )–small cancellation free products. We build upon a result of Martin and Steenbock who prove an analogous result in the more specialized setting of groups acting properly and cocompactly on Gromov hyperbolic CAT(0) cube complexes. Our methods make use of the same blown-up complex of groups to construct a candidate collection of walls. However, rather than arguing…

## References

SHOWING 1-10 OF 78 REFERENCES

A combination theorem for cubulation in small cancellation theory over free products

- Mathematics
- 2014

We prove that a group obtained as a quotient of the free product of finitely many cubulable groups by a finite set of relators satisfying the classical $C'(1/6)$--small cancellation condition is…

Complete square complexes

- Mathematics
- 2007

We study groups which act cocompactly and properly discontinuously on the direct product of two trees. This class of groups turns out to be much richer than one might expect.
An interplay is…

Acylindrically hyperbolic groups and their quasi-isometrically embedded subgroups

- Mathematics
- 2021

We abstract the notion of an A/QI triple from a number of examples in geometric group theory. Such a triple (G,X,H) consists of a group G acting on a Gromov hyperbolic space X, acylindrically along a…

Non-positively curved complexes of groups and boundaries

- Mathematics
- 2014

Given a complex of groups over a finite simplicial complex in the sense of Haefliger, we give conditions under which it is possible to build an EZ ‐structure in the sense of Farrell and Lafont for…

Relatively geometric actions on CAT$\operatorname{CAT}$ (0) cube complexes

- MathematicsJournal of the London Mathematical Society
- 2022

We develop the foundations of the theory of relatively geometric actions of relatively hyperbolic groups on CAT$\operatorname{CAT}$ (0) cube complexes, a notion introduced in our previous work…

Separation and Relative Quasi-convexity Criteria for Relatively Geometric Actions

- Mathematics
- 2021

Bowditch characterized relative hyperbolicity in terms of group actions on fine hyperbolic graphs with finitely many edge orbits and finite edge stabilizers. In this paper, we define generalized fine…

The virtual Haken conjecture

- Mathematics
- 2012

We prove that cubulated hyperbolic groups are virtually special. The proof relies on results of Haglund and Wise which also imply that they are linear groups, and quasi-convex subgroups are…

Finite and Infinite Quotients of Discrete and Indiscrete Groups

- MathematicsGroups St Andrews 2017 in Birmingham
- 2019

These notes are devoted to lattices in products of trees and related topics. They provide an introduction to the construction, by M. Burger and S. Mozes, of examples of such lattices that are simple…

Acylindrical accessibility for groups

- Mathematics
- 1997

Abstract.We define the notion of acylindrical graph of groups of a group. We bound the combinatorics of these graphs of groups for f.g. freely indecomposable groups. Our arguments imply the…