Anne Lonjou - Sur l'hyperbolicité de graphes associés au groupe de Cremona

epiga:4895 - Épijournal de Géométrie Algébrique, September 23, 2019, Volume 3 -
Sur l'hyperbolicité de graphes associés au groupe de Cremona

Authors: Anne Lonjou

To reinforce the analogy between the mapping class group and the Cremona group of rank $2$ over an algebraic closed field, we look for a graph analoguous to the curve graph and such that the Cremona group acts on it non-trivially. A candidate is a graph introduced by D. Wright. However, we demonstrate that it is not Gromov-hyperbolic. This answers a question of A. Minasyan and D. Osin. Then, we construct two graphs associated to a Vorono\"i tesselation of the Cremona group introduced in a previous work of the autor. We show that one is quasi-isometric to the Wright graph. We prove that the second one is Gromov-hyperbolic.

Volume: Volume 3
Published on: September 23, 2019
Accepted on: September 23, 2019
Submitted on: October 18, 2018
Keywords: Mathematics - Group Theory,Mathematics - Algebraic Geometry


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