A homological upper bound on critical probabilities for hyperbolic percolation

Nicolas Delfosse; Gilles Zémor

doi:10.4171/aihpd/27

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A homological upper bound on critical probabilities for hyperbolic percolation

Nicolas Delfosse, Gilles Zémor

Annales de l’Institut Henri Poincaré D Combinatorics Physics and their Interactions2016doi:10.4171/aihpd/27

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Abstract

We study bond percolation for a family of infinite hyperbolic graphs. We relate percolation to the appearance of homology in finite versions of these graphs. As a consequence, we derive an upper bound on the critical probabilities of the infinite graphs.

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Nicolas Delfosse#1 Gilles Zémor#2

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