• 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}
}
. 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. 

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References

SHOWING 1-10 OF 39 REFERENCES

Cubulating Surface-by-free Groups

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

. 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

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

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