Presented by:
Alessandro Sisto
Date:
Thursday 9th February 2017 - 10:00 to 12:00
Venue:
INI Seminar Room 2
Abstract:
The notion of hierarchically hyperbolic space provides a
common framework to study mapping class groups, Teichmueller spaces with either
the Teichmueller or the Weil-Petersson metric, CAT(0) cube complexes admitting
a proper cocompact action, fundamental groups of non-geometric 3-manifolds, and
other examples.
I will discuss the result that any top-dimensional
quasi-flat in a hierarchically hyperbolic space lies within finite Hausdorff
distance from a finite union of "standard orthants", a result new for
both mapping class groups and cube complexes. Also, I will discuss how this can
be used to reduce proving quasi-isometric rigidity results to much more
manageable, (mostly) combinatorial problems that require no knowledge about the
geometry of HHSs.
Joint work with Jason Behrstock and Mark Hagen.
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