English
Action rigidity for free products of hyperbolic manifold groups
Virtualconference
Auteurs : Stark, Emily (Auteur de la Conférence)
CIRM (Editeur )
20E06 - Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
20F65 - Geometric group theory
20F67 - Hyperbolic groups and nonpositively curved groups
57M07 - Topological methods in group theory
57M10 - Covering spaces
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2159/Slides/Stark_talk.pdf
CIRM (Editeur )
Loading the player...
|
Résumé :
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.
Keywords : hyperbolic groups; commensurability; quasi-isometry classes; free products
Codes MSC : Keywords : hyperbolic groups; commensurability; quasi-isometry classes; free products
20E06 - Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
20F65 - Geometric group theory
20F67 - Hyperbolic groups and nonpositively curved groups
57M07 - Topological methods in group theory
57M10 - Covering spaces
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2159/Slides/Stark_talk.pdf
|
Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 01/06/2020 Date de captation : 22/05/2020 Sous collection : Research talks arXiv category : Group Theory ; Geometric Topology Domaine : Algebra ; Geometry ; Topology Format : MP4 (.mp4) - HD Durée : 00:33:19 Audience : Researchers Download : https://videos.cirm-math.fr/ 2020-05-22_Stark.mp4 
|
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.19637003Citer cette vidéo: Stark, Emily (2020). Action rigidity for free products of hyperbolic manifold groups. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19637003 URI : http://dx.doi.org/10.24350/CIRM.V.19637003 |
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] 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] Quasi-actions and almost normal subgroups / Auteur de la Conférence Margolis, Alex.
- [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
- BURGER, Marc et MOZES, Shahar. Lattices in product of trees. Publications Mathématiques de l'IHÉS, 2000, vol. 92, p. 151-194. - http://www.numdam.org/item?id=PMIHES_2000__92__151_0
- CHOW, Richard. Groups quasi-isometric to complex hyperbolic space. Transactions of the American Mathematical Society, 1996, vol. 348, no 5, p. 1757-1769. - http://dx.doi.org/10.1090/S0002-9947-96-01522-X
- DUNWOODY, Martin J. The accessibility of finitely presented groups. Inventiones mathematicae, 1985, vol. 81, no 3, p. 449-457. - https://doi.org/10.1007/s00222-014-0552-x
- HINKKANEN, Aimo. Uniformly quasisymmetric groups. Proceedings of the London Mathematical Society, 1985, vol. 3, no 2, p. 318-318. - https://doi.org/10.1112/plms/s3-51.2.318
- HINKKANEN, A.The structure of certain quasisymmetric groups. Mem. Amer. Math. Soc.,Y, 1990, vol. 83, no 422, p. 1-87. - https://bookstore.ams.org/memo-83-422/
- LEIGHTON, Frank Thomson. Finite common coverings of graphs. Journal of Combinatorial Theory, Series B, 1982, vol. 33, no 3, p. 231-238. - https://doi.org/10.1016/0095-8956(82)90042-9
- 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
- PANSU, Pierre. Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un. Annals of Mathematics, 1989, p. 1-60. - https://www.jstor.org/stable/1971484
- PAPASOGLU, Panos et WHYTE, Kevin. Quasi-isometries between groups with infinitely many ends. Commentarii Mathematici Helvetici, 2002, vol. 77, no 1, p. 133-144. - https://doi.org/10.1007/s00014-002-8334-2
- SHEPHERD, Sam, GARDAM, Giles, et WOODHOUSE, Daniel J. Two generalisations of Leighton's Theorem. arXiv preprint arXiv:1908.00830, 2019. - https://arxiv.org/abs/1908.00830
- STARK, Emily et WOODHOUSE, Daniel J. Quasi‐isometric groups with no common model geometry. Journal of the London Mathematical Society, 2019, vol. 99, no 3, p. 853-871. - https://doi.org/10.1112/jlms.12189
- TUKIA, P. On quasiconformal groups. J. Anal. Math. 1986, vol 46, p. 318–346. - https://doi.org/10.1007/BF02796595
