Cubical geometry via hyperbolicity
Groups acting on CAT(0) spaces September 27, 2016 - September 30, 2016
Location: SLMath: Eisenbud Auditorium
CAT(0) space
Riemannian geometry
negative curvature manifolds
hyperbolic manifold
Symmetric space
buildings and complexes
54C40 - Algebraic properties of function spaces in general topology [See also 46Exx]
01-11 - Research data for problems pertaining to history and biography
55R35 - Classifying spaces of groups and $H$H-spaces in algebraic topology
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I will discuss a collection of hyperbolic graphs associated to a CAT(0) cube complex and explain how the geometry of the cube complex can be recovered -- up to quasi-isometry -- from its shadows on these graphs. I will explain how this mirrors the Masur-Minsky theory enabling the study of the mapping class group of a surface via projections to curve graphs of subsurfaces. I'll then define "hierarchical hyperbolicity", which is a common generalisation of these two classes of examples, and discuss some applications. This is based on joint work with J. Behrstock and A. Sisto
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14613
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