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Action rigidity for free products of hyperbolic manifold groups
Virtualconference
Authors : Stark, Emily (Author of the conference)
CIRM (Publisher )
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
Additional resources :
https://www.cirm-math.fr/RepOrga/2159/Slides/Stark_talk.pdf
CIRM (Publisher )
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Abstract :
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
MSC Codes : 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
Additional resources :
https://www.cirm-math.fr/RepOrga/2159/Slides/Stark_talk.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 01/06/2020 Conference Date : 22/05/2020 Subseries : Research talks arXiv category : Group Theory ; Geometric Topology Mathematical Area(s) : Algebra ; Geometry ; Topology Format : MP4 (.mp4) - HD Video Time : 00:33:19 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/ 2020-05-22_Stark.mp4 
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Information on the Event
Event Title : Virtual Geometric Group Theory conference / Rencontre virtuelle en géométrie des groupesEvent Organizers : Chatterji, Indira ; Paris, Luis ; Vogtmann, Karen Dates : 01/06/2020 - 05/06/2020 Event Year : 2020 Event URL : https://conferences.cirm-math.fr/virtual...
Citation Data
DOI : 10.24350/CIRM.V.19637003Cite this video as: 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 |
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