Hyperbolic spaces for $\mathrm{CAT}(0)$ groups
Davide Spriano (Oxford)
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 )
Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/
The talks start five minutes after the hour. Talks are typically 55 minutes long, including time for questions.
Organizers: | Saul Schleimer*, Robert Kropholler* |
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