7 citations · 12 across the 8 of their papers we have counts for
9 papers
From cut sets to cube complexes
Matthew Haulmark, Jason Fox Manning
In this paper, we obtain an action on a cube complex from an action on a path-connected topological space with a system of divisions. In the settings of hyperbolic groups or relati…
Minimal Volume Entropy of RAAG's
Matthew Haulmark, Kevin Schreve
Bregman and Clay recently characterized which right-angled Artin groups with geometric dimension 2 have vanishing minimal volume entropy. In this note, we extend this characterizat…
On canonical splittings of relatively hyperbolic groups
Matthew Haulmark, G. Christopher Hruska
A JSJ decomposition of a group is a splitting that allows one to classify all possible splittings of the group over a certain family of edge groups. Although JSJ decompositions are…
Piecewise Visual, Linearly Connected Metrics on Boundaries of Relatively Hyperbolic Groups
Matthew Haulmark, Michael L. Mihalik
Suppose a finitely generated group is hyperbolic relative to a set of proper finitely generated subgroups of . Established results in the literature imply that…
Right-angled Coxeter groups with non-planar boundary
Pallavi Dani, Matthew Haulmark, Genevieve Walsh
We investigate the planarity of the boundaries of right-angled Coxeter groups. We show that non-planarity of the defining graph does not necessarily imply non-planarity of every bo…
Nonhyperbolic Coxeter groups with Menger curve boundary (with erratum)
Matthew Haulmark, G. Christopher Hruska, Bakul Sathaye
A generic finite presentation defines a word hyperbolic group whose boundary is homeomorphic to the Menger curve. In this article, we produce the first known examples of non-hyperb…
On the relative hyperbolicity and manifold structure of certain right-angled Coxeter groups
Matthew Haulmark, Hoang Thanh Nguyen, Hung Cong Tran
In this article, we study the manifold structure and the relatively hyperbolic structure of right-angled Coxeter groups with planar nerves. We then apply our results to the quasi-i…
Local cut points and splittings of relatively hyperbolic groups
Matthew Haulmark
In this paper we show that the existence of a non-parabolic local cut point in the Bowditch boundary of a relatively hyperbolic group impl…
Boundary classification and 2-ended splittings of groups with isolated flats
Matthew Haulmark
In this paper we provide a classification theorem for 1-dimensional boundaries of groups with isolated flats. Given a group acting geometrically on a space with is…