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Polynomial hyperbolicity and products of free groups
Anthony Genevois
In this article, we define a locally finite graph as -polynomially hyperbolic if there exists a Lipschitz map to some hyperbolic space satisfying the follow…
Relative numbers of ends and quasi-median graphs
Anthony Genevois
Given a finitely generated and a subgraph , the relative number of ends is the number of ends of a Schreier graph and the number of coend…
Virtual splittings of right-angled Artin groups
Oussama Bensaid, Anthony Genevois, Romain Tessera
In this article, we determine, given a finite graph and an integer , when a right-angled Artin group virtually splits over an abelian subgroup of rank . Mor…
Coarse separation and splittings in right-angled Artin groups
Oussama Bensaid, Anthony Genevois, Romain Tessera
In this article, we characterise geometrically when a right-angled Artin group splits over an abelian subgroup. More precisely, given a finite graph , we show that splits…
Coarse separation and splittings in hyperbolic groups
Oussama Bensaid, Anthony Genevois, Romain Tessera
We study coarse separation in one-ended hyperbolic groups from a quantitative point of view, focusing on the volume growth of separating subsets. We prove that a one-ended hyperbol…
Asymptotically rigid mapping class groups III: Presentations and isomorphisms
Anthony Genevois, Anne Lonjou, Christian Urech
This article is dedicated to the computation of an explicit presentation of some asymptotically rigid mapping class groups, namely the braided Higman-Thompson groups. To do so, we…
An illustrated introduction to the coarse topology of lamplighters
Anthony Genevois
Roughly speaking, lamplighter graphs encode the possible configurations of a lamplighter that moves along a given graph and that modifies the colours of lamps at vertices. This art…
Lamplighter-like geometry of groups
Anthony Genevois, Romain Tessera
In this article, we introduce halo products as a natural generalisation of wreath products. They also encompass lampshuffler groups and lampcloner grou…
Coarse separation and large-scale geometry of wreath products
Oussama Bensaid, Anthony Genevois, Romain Tessera
In this article, we introduce and study a natural notion of coarse separation for metric spaces, with an emphasis on coarse separation by subspaces of polynomial or subexponential…
Folding median graphs
Anthony Genevois, Yassine Guerch, Romain Tessera
Extending Stallings' foldings of trees, we show in this article that every parallel-preserving map between median graphs factors as an isometric embedding through a sequence of ele…
Why CAT(0) cube complexes should be replaced with median graphs
Anthony Genevois
In this note, we discuss and motivate the use of the terminology ``median graphs'' in place of ``CAT(0) cube complexes'' in geometric group theory.