149 citations · 710 across the 38 of their papers we have counts for
26 papers · 1 filter
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…
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…
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…
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…
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…
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…
Hierarchically hyperbolic spaces II: Combination theorems and the distance formula
Jason Behrstock, Mark F. Hagen, Alessandro Sisto
We introduce a number of tools for finding and studying \emph{hierarchically hyperbolic spaces (HHS)}, a rich class of spaces including mapping class groups of surfaces, Teichmülle…
Quantifying separability in virtually special groups
Mark F. Hagen, Priyam Patel
We give a new, effective proof of the separability of cubically convex-cocompact subgroups of special groups. As a consequence, we show that if is a virtually compact special h…
Cubulating hyperbolic free-by-cyclic groups: the general case
Mark F. Hagen, Daniel T. Wise
Let be an automorphism of the finite-rank free group . Suppose that is word-hyperbolic. Then acts freely and cocompactly on a CAT(…
Residual Finiteness Growths of Virtually Special Groups
Khalid Bou-Rabee, Mark F. Hagen, Priyam Patel
Let be a virtually special group. Then the residual finiteness growth of is at most linear. This result cannot be found by embedding into a special linear group. Indeed…
Thickness, relative hyperbolicity, and randomness in Coxeter groups
Jason Behrstock, Mark F. Hagen, Alessandro Sisto +1
For right-angled Coxeter groups , we obtain a condition on that is necessary and sufficient to ensure that is thick and thus not relatively hyperbolic. We show that…
Cubulating hyperbolic free-by-cyclic groups: the irreducible case
Mark F. Hagen, Daniel T. Wise
Let be a finite graph and let be an irreducible train track map whose mapping torus has word-hyperbolic fundamental group . Then acts freely and cocom…
Cubulated groups: thickness, relative hyperbolicity, and simplicial boundaries
Jason Behrstock, Mark F. Hagen
Let G be a group acting geometrically on a CAT(0) cube complex X. We prove first that G is hyperbolic relative to the collection P of subgroups if and only if the simplicial bounda…
Cocompactly cubulated crystallographic groups
Mark F. Hagen
We prove that the simplicial boundary of a CAT(0) cube complex admitting a proper, cocompact action by a virtually $\integers^n$ group is isomorphic to the hyperoctahedral triangul…