15 citations · 18 across the 8 of their papers we have counts for
10 papers
Asymptotically rigid mapping class groups III: Presentations and isomorphisms
Anthony Genevois, Anne Lonjou, Christian Urech
This article is dedicated to the computation of an explicit presentation of some asymptotically rigid mapping class groups, namely the braided Higman-Thompson groups. To do so, we…
Survey on Cremona groups from a median geometric point of view
Anne Lonjou
This expository article builds on lecture notes from a minicourse entitled "Cremona groups and CAT(0) cube complexes" and given by the author as part of the 2023 Riverside Workshop…
On a Theorem by Lin and Shinder through the Lens of Median Geometry
Anthony Genevois, Anne Lonjou, Christian Urech
Recently, Lin and Shinder constructed non-trivial homomorphisms from Cremona groups of rank >2 to \mathbb{Z} using motivic techniques. In this short note we propose an alternative…
Finitely generated subgroups of algebraic elements of plane Cremona groups are bounded
Anne Lonjou, Piotr Przytycki, Christian Urech
We prove that any finitely generated subgroup of the plane Cremona group consisting only of algebraic elements is of bounded degree. This follows from a more general result on `dec…
Cremona groups over finite fields, Neretin groups, and non-positively curved cube complexes
Anthony Genevois, Anne Lonjou, Christian Urech
We show that plane Cremona groups over finite fields embed as dense subgroups into Neretin groups, i.e. groups of almost automorphisms of rooted trees. We also show that if the fin…
Asymptotically rigid mapping class groups II: strand diagrams and nonpositive curvature
Anthony Genevois, Anne Lonjou, Christian Urech
In this article, we introduce a new family of groups, called Chambord groups and constructed from braided strand diagrams associated to specific semigroup presentations. It include…
Asymptotically rigid mapping class groups I: Finiteness properties of braided Thompson's and Houghton's groups
Anthony Genevois, Anne Lonjou, Christian Urech
This article is dedicated to the study of asymptotically rigid mapping class groups of infinitely-punctured surfaces obtained by thickening planar trees. Such groups include the br…
Introduction to a small cancellation theorem
Stéphane Lamy, Anne Lonjou
This note is intended as an introduction to two previous works respectively by Dahmani, Guirardel, Osin, and by Cantat, Lamy. We give two proofs of a Small Cancellation Theorem for…
Actions of Cremona groups on CAT(0) cube complexes
Anne Lonjou, Christian Urech
For each d we construct CAT(0) cube complexes on which Cremona groups rank d act by isometries. From these actions we deduce new and old group theoretical and dynamical results abo…
Elements generating a proper normal subgroup of the Cremona group
Serge Cantat, Vincent Guirardel, Anne Lonjou
Consider an algebraically closed field k and the Cremona group of all birational transformations of the projective plane over k. We characterize infinite order elements of this gro…