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Hierarchically hyperbolic structures on cube complexes and applications

Groups acting on CAT(0) spaces September 27, 2016 - September 30, 2016

September 28, 2016 (10:30 AM PDT - 11:20 AM PDT)
Speaker(s): Alessandro Sisto (ETH Zürich)
Location: MSRI: Simons Auditorium



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

26814?type=thumb Sisto.Notes 840 KB application/pdf Download
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