Weak forms of amenability for CAT(0) cubical groups
Amenability, coarse embeddability and fixed point properties December 06, 2016 - December 09, 2016
Location: MSRI: Simons Auditorium
CAT(0)
cube complex
k-amenability
Amenability
a-T-menability
hyperbolic groups
Cayley graphs
fixed point properties
geometric group theory
Banach space
group cohomology
index theory
expander graph
non-commutative geometry
20F65 - Geometric group theory [See also 05C25, 20E08, 57Mxx]
43-XX - Abstract harmonic analysis {For other analysis on topological and Lie groups, see 22Exx}
46-XX - Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx}
57-XX - Manifolds and cell complexes {For complex manifolds, see 32Qxx}
14638
A group which act properly on a CAT(0) cubical complex, while not necessarily amenable, satisfies several weak forms of amenability: such a group is a-T-menable, weakly amenable and K-theoretically amenable. In the talk, based on joint work with J. Brodzki and N. Higson, I will describe a proof of K-amenability which finds its roots in earlier work of P. Julg and A. Valette on groups acting on trees. I will focus on the geometric constructions involved, and will keep the analytic complications to a minimum
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14638
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