Abstract of a paper by U. Bader, A. Furman, T. Gelander, and N. Monod
This is an announcement for the paper "Property (T) and rigidity for actions on Banach spaces" by U. Bader, A. Furman, T. Gelander, and N. Monod. Abstract: We study property (T) and the fixed point property for actions on $L^p$ and other Banach spaces. We show that property (T) holds when $L^2$ is replaced by $L^p$ (and even a subspace/quotient of $L^p$), and that in fact it is independent of $1\leq p<\infty$. We show that the fixed point property for $L^p$ follows from property (T) when $1<p< 2+\e$. For simple Lie groups and their lattices, we prove that the fixed point property for $L^p$ holds for any $1< p<\infty$ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive Banach spaces. Archive classification: Group Theory; Functional Analysis The source file(s), ftlp14.tex: 137939 bytes, is(are) stored in gzipped form as 0506361.gz with size 43kb. The corresponding postcript file has gzipped size 152kb. Submitted from: monod@math.uchicago.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.GR/0506361 or http://arXiv.org/abs/math.GR/0506361 or by email in unzipped form by transmitting an empty message with subject line uget 0506361 or in gzipped form by using subject line get 0506361 to: math@arXiv.org.
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Dale Alspach