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Quasi-flats in hierarchically hyperbolic spaces

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NPC - Non-positive curvature group actions and cohomology

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 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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