English
Quasi-actions and almost normal subgroups
Virtualconference
Auteurs : Margolis, Alex (Auteur de la Conférence)
CIRM (Editeur )
20E08 - Groups acting on trees
20F65 - Geometric group theory
20J05 - Homological methods in group theory
57M07 - Topological methods in group theory
Ressources complémentaires :
https://conferences.cirm-math.fr/uploads/1/6/6/4/16648158/pres.pdf
CIRM (Editeur )
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Résumé :
If a group G acts isometrically on a metric space X and Y is any metric space that is quasi-isometric to X, then G quasi-acts on Y. A fundamental problem in geometric group theory is to straighten (or quasi-conjugate) a quasi-action to an isometric action on a nice space. We will introduce and investigate discretisable spaces, those for which every cobounded quasi-action can be quasi-conjugated to an isometric action of a locally finite graph. Work of Mosher-Sageev-Whyte shows that free groups have this property, but it holds much more generally. For instance, we show that every hyperbolic group is either commensurable to a cocompact lattice in rank one Lie group, or it is discretisable.
We give several applications and indicate possible future directions of this ongoing work, particularly in showing that normal and almost normal subgroups are often preserved by quasi-isometries. For instance, we show that any finitely generated group quasi-isometric to a Z-by-hyperbolic group is Z-by-hyperbolic. We also show that within the class of residually finite groups, the class of central extensions of finitely generated abelian groups by hyperbolic groups is closed under quasi-isometries.
Keywords : Quasi-action; quasi-isometry; almost normal; hyperbolic
Codes MSC : We give several applications and indicate possible future directions of this ongoing work, particularly in showing that normal and almost normal subgroups are often preserved by quasi-isometries. For instance, we show that any finitely generated group quasi-isometric to a Z-by-hyperbolic group is Z-by-hyperbolic. We also show that within the class of residually finite groups, the class of central extensions of finitely generated abelian groups by hyperbolic groups is closed under quasi-isometries.
Keywords : Quasi-action; quasi-isometry; almost normal; hyperbolic
20E08 - Groups acting on trees
20F65 - Geometric group theory
20J05 - Homological methods in group theory
57M07 - Topological methods in group theory
Ressources complémentaires :
https://conferences.cirm-math.fr/uploads/1/6/6/4/16648158/pres.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 01/06/2020 Date de captation : 27/05/2020 Sous collection : Research talks arXiv category : Geometric Topology ; Group Theory Domaine : Geometry ; Topology Format : MP4 (.mp4) - HD Durée : 00:33:48 Audience : Researchers ; General Public Download : https://videos.cirm-math.fr/2020-05-27_Margolis.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Virtual Geometric Group Theory conference / Rencontre virtuelle en géométrie des groupesOrganisateurs de la rencontre : Chatterji, Indira ; Paris, Luis ; Vogtmann, Karen Dates : 01/06/2020 - 05/06/2020 Année de la rencontre : 2020 URL Congrès : https://conferences.cirm-math.fr/virtual...
Données de citation
DOI : 10.24350/CIRM.V.19636503Citer cette vidéo: Margolis, Alex (2020). Quasi-actions and almost normal subgroups. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19636503 URI : http://dx.doi.org/10.24350/CIRM.V.19636503 |
Voir aussi
- [Virtualconference] Incoherence of free-by-free and surface-by-free groups / Auteur de la Conférence Walsh, Genevieve.
- [Virtualconference] Automorphism groups of Coxeter groups do not have Kazhdan's property (T) / Auteur de la Conférence Varghese, Olga.
- [Virtualconference] Action rigidity for free products of hyperbolic manifold groups / Auteur de la Conférence Stark, Emily.
- [Virtualconference] Intersections and joins of subgroups in free groups / Auteur de la Conférence Soroko, Ignat.
- [Virtualconference] Effectively generating RAAGs in MCGs / Auteur de la Conférence Runnels, Ian.
- [Virtualconference] Parabolic subgroups of infinite type Artin groups / Auteur de la Conférence Morris-Wright, Rose.
- [Virtualconference] Action of the Cremona group on a CAT(0) cube complex / Auteur de la Conférence Lonjou, Anne.
- [Virtualconference] Right-angled Coxeter groups commensurable to right-angled Artin groups / Auteur de la Conférence Levcovitz, Ivan.
- [Virtualconference] Computing fibring of 3-manifolds and free-by-cyclic groups / Auteur de la Conférence Kielak, Dawid.
- [Virtualconference] Shortcut graphs and groups / Auteur de la Conférence Hoda, Nima.
- [Virtualconference] Spin mapping class groups and curve graphs / Auteur de la Conférence Hamenstädt, Ursula.
- [Virtualconference] Spaces of cubulations / Auteur de la Conférence Fioravanti, Elia.
- [Virtualconference] Complexes of parabolic subgroups for Artin groups / Auteur de la Conférence Cumplido Cabello, Maria.
- [Virtualconference] Quasi-parabolic structures on groups / Auteur de la Conférence Balasubramanya, Sahana.
Bibliographie
- KAPOVICH, Michael, KLEINER, Bruce, et LEEB, Bernhard. Quasi-isometries and the de Rham decomposition. Topology, 1998, vol. 37, no 6, p. 1193-1211. - https://doi.org/10.1016/S0040-9383(97)00091-8
- MOSHER, Lee, SAGEEV, Michah, et WHYTE, Kevin. Quasi-actions on trees I. Bounded valence. Annals of mathematics, 2003, p. 115-164. - https://www.jstor.org/stable/3597155
- MARGOLIS, Alexander. The geometry of groups containing almost normal subgroups. arXiv preprint arXiv:1905.03062, 2019. - https://arxiv.org/abs/1905.03062
- MARGOLIS, Alexander. Discretisable quasi-actions. in preparation (2020) -
