论与克雷莫纳群相关的图的双曲性

IF 0.9 Q2 MATHEMATICS Epijournal de Geometrie Algebrique Pub Date : 2018-02-08 DOI:10.46298/epiga.2019.volume3.4895

Anne Lonjou

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引用次数: 2

摘要

为了加强映射类群与代数闭域上秩$2$的cremonaggroup之间的相似性，我们寻找与曲线图相似的图形，并且使得Cremona群对其起非平凡的作用。一个候选图是D. Wright介绍的。然而，我们证明了它不是格罗莫夫双曲。这回答了a . minasyan和D. Osin的一个问题。然后，我们构造了两个图，这些图与作者在之前的工作中介绍的Cremona群的Vorono本身关联。我们证明它是莱特图的准等距。我们证明了第二步是格罗莫夫双曲的。评论:29页，en Fran\c{c}ais

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Sur l'hyperbolicit\'e de graphes associ\'es au groupe de Cremona

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. Comment: 29 pages, en Fran\c{c}ais

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