Events for 05/04/2016 from all calendars

Noncommutative Geometry Seminar

Time: 2:00PM - 3:00PM

Location: BLOC 628

Speaker: Alan Czuroń, IMPAN

Title: Property (FL_q) implies Property (FL_p) for p < q, p ≠ 2.

Abstract: It is known that for σ-compact groups, Kazhdan's Property (T) is equivalent to Serre's Property FH, a condition related to isometric affine actions of a group on a Hilbert space. More generally, given a Banach space B, one can define Property (FB) in terms of isometric affine actions of a group on B. It is known that groups with Property (FL_p) shares some properties with groups with Property (T), e.g., compact generation and compact abelianization. Moreover, in the case of a discrete group, Property (FL_p) implies Lubotzky's property (τ). We prove that in the case of discrete groups and discrete lp spaces, if 1 < p < q < ∞, p ≠ 2, then Property (Fl_q) implies Property (Fl_p), i.e., if every isometric affine action of G on l_q has a G-fixed point, then every isometric affine action of G on l_p has a G-fixed point.