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arXiv · 1802.02910

Sur l'hyperbolicité de graphes associés au groupe de Cremona

Anne Lonjou
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Abstract

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 Voronoï 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.

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Anne Lonjou. 2019-09-20. Sur l'hyperbolicité de graphes associés au groupe de Cremona. https://doi.org/10.46298/epiga.2019.volume3.4895

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