Open Access
2019 Pavage de Voronoï associé au groupe de Cremona
Anne Lonjou
Publ. Mat. 63(2): 521-599 (2019). DOI: 10.5565/PUBLMAT6321905


The action of the Cremona group of rank $2$ on an infinite dimensional hyperbolic space is the main recent tool to study the Cremona group. Following~the analogy with the action of $\operatorname{PSL}(2,\mathbb{Z})$ on the Poincaré half-plane, we exhibit a fundamental domain for this action by considering a Voronoi tessellation. Then we study adjacent cells to a given cell, as well as cells that share common points in the boundary at infinity.


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Anne Lonjou. "Pavage de Voronoï associé au groupe de Cremona." Publ. Mat. 63 (2) 521 - 599, 2019.


Received: 9 October 2017; Revised: 9 May 2018; Published: 2019
First available in Project Euclid: 28 June 2019

zbMATH: 07094863
MathSciNet: MR3980934
Digital Object Identifier: 10.5565/PUBLMAT6321905

Primary: 14E07 , 20F65

Keywords: Cremona group , Fundamental domain , Hyperbolic space , Voronoi tessellation

Rights: Copyright © 2019 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.63 • No. 2 • 2019
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