• Corpus ID: 249926838

# Some examples of separable convex-cocompact subgroups

@inproceedings{Hagen2022SomeEO,
title={Some examples of separable convex-cocompact subgroups},
author={Mark F. Hagen and Alessandro Sisto},
year={2022}
}
• Published 22 June 2022
• Mathematics
. Reid asked whether all convex-cocompact subgroups of mapping class groups are separable. Using a construction of Manning-Mj-Sageev, we give examples of separable convex- cocompact subgroups that are free of arbitrary ﬁnite rank, while prior examples seem to all be virtually cyclic.

## References

SHOWING 1-10 OF 39 REFERENCES

### Cubulating Surface-by-free Groups

• Mathematics
• 2019
Let $$1 \to H \to G \to Q \to 1$$ be an exact sequence where $H= \pi_1(S)$ is the fundamental group of a closed surface $S$ of genus greater than one, $G$ is hyperbolic and $Q$ is finitely generated

### 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

### A combinatorial take on hierarchical hyperbolicity and applications to quotients of mapping class groups

• Mathematics
• 2020
We give a simple combinatorial criterion, in terms of an action on a hyperbolic simplicial complex, for a group to be hierarchically hyperbolic. We apply this to show that quotients of mapping class

### Cubulations de variétés hyperboliques compactes

Cette these est une contribution au domaine des cubulations de groupes hyperboliques au sens de Gromov. Nous nous interessons au cas particulier des groupes fondamentaux de varietes hyperboliques

### The Structure of Groups with a Quasiconvex Hierarchy

Let $G$ be a word-hyperbolic group with a quasiconvex hierarchy. We show that $G$ has a finite index subgroup $G'$ that embeds as a quasiconvex subgroup of a right-angled Artin group. It follows

### 1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs

• Mathematics
• 2015
We describe unicorn paths in the arc graph and show that they form 1-slim triangles and are invariant under taking subpaths. We deduce that all arc graphs are 7-hyperbolic. Considering the same paths