24 citations · 111 across the 23 of their papers we have counts for
23 papers · 1 filter
A Deligne complex for virtual Artin groups
Federica Gavazzi, Alexandre Martin
Virtual Artin groups were recently introduced by Bellingeri-Paris-Thiel as a generalisation of virtual braid groups. In this article, we initiate a geometric study of these groups…
Homomorphisms between XL-type Artin groups
Martín Blufstein, Alexandre Martin, Nicolas Vaskou
We study homomorphisms between XL-type Artin groups and show that, in a suitable sense, a generic Artin group is both hopfian and co-hopfian. For XL-type Artin groups over complete…
Acylindrical hyperbolicity for Artin groups with a visual splitting
Ruth Charney, Alexandre Martin, Rose Morris-Wright
We establish a criterion that implies the acylindrical hyperbolicity of many Artin groups admitting a visual splitting. This gives a variety of new examples of acylindrically hyper…
Characterising large-type Artin groups
Alexandre Martin, Nicolas Vaskou
We show that the class of large-type Artin groups is invariant under isomorphism, in stark contrast with the corresponding situation for Coxeter groups. We obtain this result by pr…
The Tits Alternative for two-dimensional Artin groups and Wise's Power Alternative
Alexandre Martin
We show that two-dimensional Artin groups satisfy a strengthening of the Tits alternative: their subgroups either contain a non-abelian free group or are virtually free abelian of…
Extra-large type Artin groups are hierarchically hyperbolic
Mark Hagen, Alexandre Martin, Alessandro Sisto
We show that Artin groups of extra-large type, and more generally Artin groups of large and hyperbolic type, are hierarchically hyperbolic. This implies in particular that these gr…
Parabolic subgroups of large-type Artin groups
María Cumplido, Alexandre Martin, Nicolas Vaskou
We show that the geometric realisation of the poset of proper parabolic subgroups of a large-type Artin group has a systolic geometry. We use this geometry to show that the set of…
Abelian subgroups of two-dimensional Artin groups
Alexandre Martin, Piotr Przytycki
We classify abelian subgroups of two-dimensional Artin groups.
A combinatorial take on hierarchical hyperbolicity and applications to quotients of mapping class groups
Jason Behrstock, Mark Hagen, Alexandre Martin +1
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 quotient…
Tits alternative for Artin groups of type FC
Alexandre Martin, Piotr Przytycki
Given a group action on a finite-dimensional CAT(0) cube complex, we give a simple criterion phrased purely in terms of cube stabilisers that ensures that the group satisfies the s…
Acylindrical actions for two-dimensional Artin groups of hyperbolic type
Alexandre Martin, Piotr Przytycki
For a two-dimensional Artin group whose associated Coxeter group is hyperbolic, we prove that the action of on the hyperbolic space obtained by coning off certain subcomple…
Automorphisms of graph products of groups from a geometric perspective
Anthony Genevois, Alexandre Martin
This article studies automorphism groups of graph products of arbitrary groups. We completely characterise automorphisms that preserve the set of conjugacy classes of vertex groups…
A combination theorem for combinatorially non-positively curved complexes of hyperbolic groups
Alexandre Martin, Damian Osajda
We prove a combination theorem for hyperbolic groups, in the case of groups acting on complexes displaying combinatorial features reminiscent of non-positive curvature. Such comple…
Automorphism groups of cyclic products of groups
Anthony Genevois, Alexandre Martin
This article initiates a geometric study of the automorphism groups of general graph products of groups, and investigates the algebraic and geometric structure of automorphism grou…
A note on the acylindrical hyperbolicity of groups acting on CAT(0) cube complexes
Indira Chatterji, Alexandre Martin
We study the acylindrical hyperbolicity of groups acting by isometries on CAT(0) cube complexes, and obtain simple criteria formulated in terms of stabilisers for the action. Namel…
Quasi-isometries Between Groups with Two-Ended Splittings
Christopher H. Cashen, Alexandre Martin
We construct `structure invariants' of a one-ended, finitely presented group that describe the way in which the factors of its JSJ decomposition over two-ended subgroups fit togeth…
On the acylindrical hyperbolicity of the tame automorphism group of
Alexandre Martin
We introduce the notion of über-contracting element, a strengthening of the notion of strongly contracting element which yields a particularly tractable criterion to show the acyli…
Acylindrical actions on CAT(0) square complexes
Alexandre Martin
For group actions on hyperbolic CAT(0) square complexes, we show that the acylindricity of the action is equivalent to a weaker form of acylindricity phrased purely in terms of sta…
On the cubical geometry of Higman's group
Alexandre Martin
We investigate the cocompact action of Higman's group on a CAT(0) square complex associated to its standard presentation. We show that this action is in a sense intrinsic, which al…
A combination theorem for cubulation in small cancellation theory over free products
Alexandre Martin, Markus Steenbock
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 --small cancellatio…
Finite index subgroups without unique product in graphical small cancellation groups
Dominik Gruber, Alexandre Martin, Markus Steenbock
We construct torsion-free hyperbolic groups without unique product whose subgroups up to some given finite index are themselves non-unique product groups. This is achieved by gener…
Combination of classifying spaces for proper actions
Alexandre Martin
Given a group action on a simplicial complex such that each simplex stabiliser admits a cocompact model of classifying space for proper actions, we give conditions implying the exi…
Complexes of groups and geometric small cancellation over graphs of groups
Alexandre Martin
We explain and generalise a construction due to Gromov to realise geometric small cancellation groups over graphs of groups as fundamental groups of non-positively curved 2-dimensi…