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A Note on Fine Graphs and Homological Isoperimetric Inequalities

  • Eduardo Martínez-Pedroza (a1)

Abstract

In the framework of homological characterizations of relative hyperbolicity, Groves and Manning posed the question of whether a simply connected 2-complex $X$ with a linear homological isoperimetric inequality, a bound on the length of attachingmaps of 2-cells, and finitely many 2-cells adjacent to any edge must have a fine 1-skeleton. We provide a positive answer to this question. We revisit a homological characterization of relative hyperbolicity and show that a group $G$ is hyperbolic relative to a collection of subgroups $P$ if and only if $G$ acts cocompactly with finite edge stabilizers on a connected 2-dimensional cell complex with a linear homological isoperimetric inequality and $P$ is a collection of representatives of conjugacy classes of vertex stabilizers.

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A Note on Fine Graphs and Homological Isoperimetric Inequalities

  • Eduardo Martínez-Pedroza (a1)

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