CAT(0) cube complexes and inner amenability

Autor: Robin Tucker-Drob, Phillip Wesolek, Bruno Duchesne

Publikováno v: Groups, Geometry, and Dynamics
Groups, Geometry, and Dynamics, European Mathematical Society, 2021, ⟨10.4171/GGD/601⟩

International audience; We here consider inner amenability from a geometric and group theoretical perspective. We prove that for every non-elementary action of a group G on a finite dimensional irreducible CAT(0) cube complex, there is a nonempty G-i

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8f4e7fa6dceed2f93a8e2572426c73b9
https://doi.org/10.4171/ggd/601

Topological properties of Wazewski dendrite groups

Autor: Bruno Duchesne

Publikováno v: Journal de l'École polytechnique — Mathématiques
Journal de l'École polytechnique — Mathématiques, École polytechnique, 2020, 7, pp.431-477. ⟨10.5802/jep.121⟩

Homeomorphism groups of generalized Wa\.zewski dendrites act on the infinite countable set of branch points of the dendrite and thus have a nice Polish topology. In this paper, we study them in the light of this Polish topology. The group of the univ

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::be0a975f16787a22057a1a8ea7fb36c1
https://hal.archives-ouvertes.fr/hal-02066642v1/document

A new lattice invariant for lattices in totally disconnected locally compact groups

Autor: Bruno Duchesne, Robin Tucker-Drob, Phillip Wesolek

Publikováno v: Israël Journal of Mathematics
Israël Journal of Mathematics, Hebrew University Magnes Press, 2020, 240, pp.539-565. ⟨10.1007/s11856-020-2072-2⟩

International audience; We introduce and explore a natural rank for totally disconnected locally compact groups called the bounded conjugacy rank. This rank is shown to be a lattice invariant for lattices in sigma compact totally disconnected locally

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f9b1bd4151816e863216aeb0b498f578
https://hal.archives-ouvertes.fr/hal-01916002/document

Representations of infinite dimension orthogonal groups of quadratic forms with finite index

Autor: Bruno Duchesne

Publikováno v: HAL
Annales de la Faculté des Sciences de Toulouse. Mathématiques.
Annales de la Faculté des Sciences de Toulouse. Mathématiques., Université Paul Sabatier _ Cellule Mathdoc In press

We study representations $G\to H$ where $G$ is either a simple Lie group with real rank at least 2 or an infinite dimensional orthogonal group of some quadratic form of finite index at least 2 and $H$ is such an orthogonal group as well. The real, co

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::29a81430d1eafeb42c9dd9bcda128bfa
http://arxiv.org/abs/1907.09803

Kaleidoscopic groups: permutation groups constructed from dendrite homeomorphisms

Autor: Bruno Duchesne, Phillip Wesolek, Nicolas Monod

Publikováno v: Fundamenta Mathematicae
Fundamenta Mathematicae, Instytut Matematyczny, Polskiej Akademii Nauk, 2019, 247 (3), pp.229-274. ⟨10.4064/fm702-4-2019⟩

Given a transitive permutation group, a fundamental object for studying its higher transitivity properties is the permutation action of its isotropy subgroup. We reverse this relationship and introduce a universal construction of infinite permutation

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7c663d3981dadcc56c39a292d49d3b89
http://arxiv.org/abs/1801.09787