• Corpus ID: 245144985

Banach Zuk's criterion for partite complexes with application to random groups

  title={Banach Zuk's criterion for partite complexes with application to random groups},
  author={Izhar Oppenheim},
We prove a Banach version of Żuk’s criterion for groups acting on partite simplicial complexes. Using this new criterion we derive a new fixed point theorem for random groups in the Gromov density model with respect to several classes of Banach spaces (L spaces, Hilbertian spaces, uniformly curved spaces). In particular, we show that for every p, a group in the Gromov density model has asymptotically almost surely property (FL) and give a sharp lower bound for the growth of the conformal… 

Round Trees and Conformal Dimension in Random Groups: low density to high density

We investigate conformal dimension for the class of infinite hyperbolic groups in the Gromov density model G dm,l of random groups with m ≥ 2 fixed generators, density 0 < d < 1 / 2 and relator length

Random groups do not have Property (T) at densities below 1/4

We prove that random groups in the Gromov density model at density d < 1 / 4 do not have Property (T), answering a conjecture of Przytycki. We also prove similar results in the k -angular model of



Garland's method with Banach coefficients

We prove a Banach version of Garland's method of proving vanishing of cohomology for groups acting on simplicial complexes. The novelty of this new version is the condition for the spectral gap of

A local characterization of Kazhdan projections and applications

We give a local characterization of the existence of Kazhdan projections for arbitary families of Banach space representations of a compactly generated locally compact group G. We also define and

Random groups and property (T): Żuk's theorem revisited

A full and rigorous proof of a theorem, stating that random groups in the Gromov density model for d > 1/3 have property (T) with high probability, is provided.

Banach space actions and L2-spectral gap

Żuk proved that if a finitely generated group admits a Cayley graph such that the Laplacian on the links of this Cayley graph has a spectral gap $> \frac{1}{2}$, then the group has property (T), or


Let F be a non archimedean local field and let G be an algebraic connected almost F-simple group over F, whose Lie algebra contains sl3(F). We prove that G(F) has strong Banach property (T) in a

Property (T) and rigidity for actions on Banach spaces

We study property (T) and the fixed-point property for actions on Lp and other Banach spaces. We show that property (T) holds when L2 is replaced by Lp (and even a subspace/quotient of Lp), and that

Towards strong Banach property (T) for SL(3,ℝ)

We prove that SL(3, ℝ) has Strong Banach property (T) in Lafforgue’s sense with respect to the Banach spaces that are θ > 0 interpolation spaces (for the complex interpolation method) between an

New Kazhdan Groups

The group of simplicial automorphisms of a Tits–Kac–Moody infinite building of thickness q associated to a cocompact reflexion group with fundamental domain a simplex, is Kazhdan for q sufficiently

On L2-cohomology and Property (T) for Automorphism Groups of Polyhedral Cell Complexes

Abstract. We present an update of Garland's work on the cohomology of certain groups, construct a class of groups many of which satisfy Kazhdan's Property (T) and show that properly discontinuous and

Vanishing of cohomology and property (T) for groups acting on weighted simplicial complexes

We extend Ballmann and Swiatkowski's work on $L^2$-cohomology of groups acting on simplicial complexes and provide further vanishing results of $L^2$-cohomologies. In particular, we give a new