6 papers
The curve complex as a coset intersection complex
Haoyang He, Eduardo Martínez-Pedroza
We show that there is a collection of subgroups of the mapping class group of a surface such that the associated coset intersection complex is quasi-isometric and homotopy equivale…
A Combination Theorem for Geodesic Coarsely Convex Group Pairs
Tomohiro Fukaya, Eduardo Martínez-Pedroza, Takumi Matsuka
The first author and Oguni introduced a class of groups of non-positive curvature, called coarsely convex group. The recent success of the theory of groups which are hyperbolic rel…
Gromov's Approximating Tree and the All-Pairs Bottleneck Paths Problem
Anders Cornect, Eduardo Martínez-Pedroza
Given a pointed metric space on points, its Gromov's approximating tree is a 0-hyperbolic pseudo-metric space such that $\mathsf{di…
The Lamplighter groups have infinite weak cop number
Anders Cornect, Eduardo Martínez-Pedroza
The weak-cop number of a graph, a variation of the cop number, is an invariant suitable for infinite graphs and is a quasi-isometric invariant. While for any $m\in\mathbb{Z}_+\cup\…
The quasi-isometry invariance of the Coset Intersection Complex
Carolyn Abbott, Eduardo Martínez-Pedroza
For a pair consisting of a group and finite collection of subgroups, we introduce a simplicial -complex called the coset intersect…
Relative Dehn fuctions, hyperbolically embedded subgroups and combination theorems
Hadi Bigdely, Eduardo Martínez-Pedroza
Consider the following classes of pairs consisting of a group and a finite collection of subgroups: $\mathcal{C}= \left\{ (G,\mathcal H) \mid \text{$\mathcal{H}$ is hyperbolically…