Hyperbolic spaces for $\mathrm{CAT}(0)$ groups

Davide Spriano (Oxford)

27-Jan-2022, 15:05-15:55 (2 years ago)

Abstract: $\mathrm{CAT}(0)$ spaces, as avatars of non-positive curvature, are both old and widely studied. Making up an important subclass are the $\mathrm{CAT}(0)$ cube complexes: spaces obtained by gluing Euclidean $n$-cubes along faces and satisfying an additional combinatorial conditions. Given such a space $X$, there are several techniques to construct associated spaces that "detect the hyperbolic behaviour" of $X$. All of these techniques rely on the combinatorial structure coming from the cubes.

In this talk we will present a new approach to construct hyperbolic spaces on which $\mathrm{CAT}(0)$ groups act. We thus obtain characterisations of rank-one elements and recover rank-rigidity results.

This is joint work with H. Petyt and A. Zalloum.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( slides )


Geometry and topology online

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