Cubical geometry via hyperbolicity
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
Symmetric space
buildings and complexes
57-XX - Manifolds and cell complexes {For complex manifolds, see 32Qxx}
58D05 - Groups of diffeomorphisms and homeomorphisms as manifolds [See also 22E65, 57S05]
14613
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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