# A topological equivalence relation for finitely presented groups

@article{Cardenas2020ATE,
title={A topological equivalence relation for finitely presented groups},
author={M. C'ardenas and Francisco F. Lasheras and Antonio Quintero and Ranja Roy},
journal={arXiv: Geometric Topology},
year={2020}
}
• M. C'ardenas, +1 author R. Roy
• Published 4 February 2020
• Mathematics
• arXiv: Geometric Topology
In this paper, we consider an equivalence relation within the class of finitely presented discrete groups attending to their asymptotic topology rather than their asymptotic geometry. More precisely, we say that two finitely presented groups $G$ and $H$ are "proper $2$-equivalent" if there exist (equivalently, for all) finite $2$-dimensional CW-complexes $X$ and $Y$, with $\pi_1(X) \cong G$ and $\pi_1(Y) \cong H$, so that their universal covers $\widetilde{X}$ and $\widetilde{Y}$ are proper $2… ## References SHOWING 1-10 OF 57 REFERENCES A Note on Group Extensions and Proper 3-Realizability • Mathematics • 2016 AbstractThe interaction between the study of three-dimensional manifolds and a particular stream of group theory has often been fruitful. In the realm of this, we recall that a finitely presented One-relator groups and proper 3-realizability • Mathematics • 2009 How different is the universal cover of a given finite 2-complex from a 3-manifold (from the proper homotopy viewpoint)? Regarding this question, we recall that a finitely presented group$G$is said Quasi-isometries between groups with infinitely many ends • Mathematics • 2002 Abstract. Let G, F be finitely generated groups with infinitely many ends and let¶$ \pi_1(\Gamma,\mathcal A), \pi_1(\Delta ,\mathcal B) \$ be graph of groups decompositions of F, G such that all edge
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