36 citations · 125 across the 10 of their papers we have counts for
12 papers
Homotopy types of complexes of hyperplanes in quasi-median graphs and applications to right-angled Artin groups
Carolyn Abbott, Anthony Genevois, Eduardo Martinez-Pedroza
In this article, we prove that, given two finite connected graphs and , if the two right-angled Artin groups and are quasi-isometric, then the infinite…
Dismantlable classifying space for the family of parabolic subgroups of a relatively hyperbolic group
Eduardo Martinez-Pedroza, Piotr Przytycki
Let be a group hyperbolic relative to a finite collection of subgroups . Let be the family of subgroups consisting of all the conjugates of subgroups i…
Subgroups of Relatively Hyperbolic Groups of Bredon Cohomological Dimension 2
Eduardo Martinez-Pedroza
A remarkable result of Gersten states that the class of hyperbolic groups of cohomological dimension is closed under taking finitely presented (or more generally ) subgro…
The Coarse Geometry of Hartnell's Firefighter Problem on Infinite Graphs
Danny Dyer, Eduardo Martinez-Pedroza, Brandon Thorne
In this article, we study Hartnell's Firefighter Problem through the group theoretic notions of growth and quasi-isometry. A graph has the -containment property if for every fin…
A note on fine graphs and homological isoperimetric inequalities
Eduardo Martinez-Pedroza
In the framework of homological characterizations of relative hyperbolicity, Groves and Manning posed the question of whether a simply connected -complex with a linear homol…
Lifting Group Actions, Equivariant Towers and Subgroups of Non-positively Curved Groups
Richard Gaelan Hanlon, Eduardo Martinez-Pedroza
If is a class of complexes closed under taking full subcomplexes and covers and is the class of groups admitting proper and cocompact actions on one-conne…
Virtual Amalgamation of Relatively Quasiconvex Subgroups
Eduardo Martinez-Pedroza, Alessandro Sisto
For relatively hyperbolic groups, we investigate conditions guaranteeing that the subgroup generated by two relatively quasiconvex subgroups and is relatively quasiconv…
Relative Quasiconvexity using Fine Hyperbolic Graphs
Eduardo Martinez-Pedroza, Daniel T. Wise
We provide a new and elegant approach to relative quasiconvexity for relatively hyperbolic groups in the context of Bowditch's approach to relative hyperbolicity using cocompact ac…
Local Quasiconvexity of Groups acting on Small Cancellation Complexes
Eduardo Martinez-Pedroza, Daniel T. Wise
Given a group acting cellularly and cocompactly on a simply-connected 2-complex, we provide a criterion establishing that all finitely generated subgroups have quasiconvex orbits.…
Separation of Relatively Quasiconvex Subgroups
Jason Fox Manning, Eduardo Martinez-Pedroza
Suppose that all hyperbolic groups are residually finite. The following statements follow: In relatively hyperbolic groups with peripheral structures consisting of finitely generat…
On Quasiconvexity and Relative Hyperbolic Structures
Eduardo Martinez-Pedroza
Let G be a group which is hyperbolic relative to a collection of subgroups A, and it is also hyperbolic relative to a collection of subgroups B. Suppose that the collection A conta…
Combination of quasiconvex subgroups of relatively hyperbolic groups
Eduardo Martinez-Pedroza
For relatively hyperbolic groups, we investigate conditions guaranteeing that the subgroup generated by two quasiconvex subgroups and is quasiconvex and isomorphic to $Q \a…