149 citations · 710 across the 38 of their papers we have counts for
39 papers
Periodic quasiflats in hierarchically hyperbolic spaces
Pénélope Azuelos, Mark Hagen
We prove a quasiflat closing theorem and a coarse flat torus theorem for hierarchically hyperbolic groups (HHGs). Namely, given an HHG , we prove that is hyperbolic if and o…
Coarse embeddings of products of trees as quasi-isometry invariants
Mark Hagen, Alessandro Sisto
We consider the maximal number of factors of a product of bushy trees that can be quasi-isometrically, or even coarsely embedded into various groups of interest, including mapping…
Characterizing hierarchically hyperbolic free by cyclic groups
Eliot Bongiovanni, Pritam Ghosh, Funda Gültepe +1
We algebraically characterize free by cyclic groups that have coarse medians, and prove that this is equivalent to the a priori stronger properties of being colourable hierarchical…
Combination theorems for Wise's power alternative
Mark Hagen, Alexandre Martin, Giovanni Sartori
We show that Wise's power alternative is stable under certain group constructions, use this to prove the power alternative for new classes of groups, and recover known results from…
Induced quasi-isometries of hyperbolic spaces, Markov chains, and acylindrical hyperbolicity
Antoine Goldsborough, Mark Hagen, Harry Petyt +2
We show that quasi-isometries of (well-behaved) hierarchically hyperbolic groups descend to quasi-isometries of their maximal hyperbolic space. This has two applications, one relat…
A Combinatorial Structure for Many Hierarchically Hyperbolic Spaces
Mark Hagen, Giorgio Mangioni, Alessandro Sisto
The combinatorial hierarchical hyperbolicity criterion is a very useful way of constructing new hierarchically hyperbolic spaces (HHSs). We show that, conversely, HHSs satisfying n…
Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups
Carolyn Abbott, Mark Hagen, Harry Petyt +1
We show that infinite cyclic subgroups of groups acting uniformly properly on injective metric spaces are uniformly undistorted. In the special case of hierarchically hyperbolic gr…
Homotopy equivalent boundaries of cube complexes
Talia Fernós, David Futer, Mark Hagen
A finite-dimensional CAT(0) cube complex is equipped with several well-studied boundaries. These include the Tits boundary (which depends on the CAT(0) metric), the Roller boun…
Equivariant hierarchically hyperbolic structures for 3-manifold groups via quasimorphisms
Mark Hagen, Jacob Russell, Alessandro Sisto +1
Behrstock, Hagen, and Sisto classified 3-manifold groups admitting a hierarchically hyperbolic space structure. However, these structures were not always equivariant with respect t…
Some examples of separable convex-cocompact subgroups
Mark Hagen, Alessandro Sisto
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 s…
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…
Projection complexes and quasimedian maps
Mark Hagen, Harry Petyt
We use the projection complex machinery of Bestvina--Bromberg--Fujiwara to study hierarchically hyperbolic groups. In particular, we show that if the group has a BBF colouring and…
Large facing tuples and a strengthened sector lemma
Mark Hagen
We prove a strengthened sector lemma for irreducible, finite-dimensional, locally finite, essential, cocompact CAT(0) cube complexes under the additional hypothesis that the comple…
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…
Deforming cubulations of hyperbolic groups
Elia Fioravanti, Mark Hagen
We describe a procedure to deform cubulations of hyperbolic groups by "bending hyperplanes". Our construction is inspired by related constructions like Thurston's Mickey Mouse exam…
A remark on thickness of free-by-cyclic groups
Mark Hagen
Let be a free group of positive, finite rank and let be a polynomial-growth automorphism. Then is strongly thick of order , where is…
Dehn filling Dehn twists
François Dahmani, Mark Hagen, Alessandro Sisto
Let be the genus-- oriented surface with punctures, with either or . We show that is acylindrically hyperbolic where is the norma…
Panel collapse and its applications
Mark F. Hagen, Nicholas W. M. Touikan
We describe a procedure called panel collapse for replacing a CAT(0) cube complex by a "lower complexity" CAT(0) cube complex whenever contains a codimension-$2…
Quasiflats in hierarchically hyperbolic spaces
Jason Behrstock, Mark F Hagen, Alessandro Sisto
The rank of a hierarchically hyperbolic space is the maximal number of unbounded factors in a standard product region. For hierarchically hyperbolic groups, this coincides with the…
On hierarchical hyperbolicity of cubical groups
Mark F Hagen, Tim Susse
Let X be a proper CAT(0) cube complex admitting a proper cocompact action by a group G. We give three conditions on the action, any one of which ensures that X has a factor system…
Meta-Evaluation of Translation Evaluation Methods: a systematic up-to-date overview
Lifeng Han, Serge Gladkoff
Starting from the 1950s, Machine Translation (MT) was challenged by different scientific solutions, which included rule-based methods, example-based and statistical models (SMT), t…
Boundaries and automorphisms of hierarchically hyperbolic spaces
Matthew G. Durham, Mark F. Hagen, Alessandro Sisto
Hierarchically hyperbolic spaces provide a common framework for studying mapping class groups of finite type surfaces, Teichmüller space, right-angled Artin groups, and many other…
Acylindrical hyperbolicity of cubical small-cancellation groups
Goulnara N. Arzhantseva, Mark F. Hagen
We provide an analogue of Strebel's classification of geodesic triangles in classical groups for groups given by Wise's cubical presentations satisfying sufficiently…
Asymptotic dimension and small-cancellation for hierarchically hyperbolic spaces and groups
Jason Behrstock, Mark F. Hagen, Alessandro Sisto
We prove that all hierarchically hyperbolic spaces have finite asymptotic dimension and obtain strong bounds on these dimensions. One application of this result is to obtain the sh…