Hierarchically hyperbolic structures on cube complexes and applications
Groups acting on CAT(0) spaces September 27, 2016 - September 30, 2016
Location: MSRI: Simons Auditorium
CAT(0) space
Riemannian geometry
negative curvature manifolds
hyperbolic manifold
mapping class groups
57-XX - Manifolds and cell complexes {For complex manifolds, see 32Qxx}
58D05 - Groups of diffeomorphisms and homeomorphisms as manifolds [See also 22E65, 57S05]
14612
A hierarchically hyperbolic structure gives a way of reducing the study of a given metric space to the study of a specified family of hyperbolic spaces. Spaces with hierarchically hyperbolic structures include CAT(0) cube complexes admitting a proper and cocompact isometric action, mapping class groups, Teichmuller spaces with either the Teichmuller or the Weil-Petersson metric and many 3-manifold groups.
I will outline what a hierarchically hyperbolic structure is and how to give one to a CAT(0) cube complex admitting a factor system, which is a "large enough" locally finite collection of convex subcomplexes. Finally, I will give applications, in particular one regarding acylindrical actions.
Based on joint works with J. Behrstock and M. Hagen
|
Sisto.Notes
|
Download |
14612
| H.264 Video |
14612.mp4
|
Download |
Please report video problems to itsupport@msri.org.
See more of our Streaming videos on our main VMath Videos page.