Proper actions of lamplighter groups associated with free groups

By Yves Cornulier, Yves Stalder, Alain Valette. 2007

46 citations recorded by the source corpus.

Abstract Given a finite group H and a free group F n , we prove that the wreath product H ≀ F n admits a metrically proper, isometric action on a Hilbert space. To cite this article: Y. de Cornulier et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/72cdbee8e440ad4e0af9effd1fbf5cbf6d12a39d

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Lp compression, traveling salesmen, and stable walks (2009, methodology): “nt and equivariant compression exponent can be diﬀerent from each other, while in many cases we know that these two invariants coincide: for example α∗ p(C 2≀F n) = α#p(C ≀F ) = max n 1 p, 1 2 o (see [21, 44]). A useful result of Aharoni, Maurey and Mityagin [1] for Abelian groups, and Gromov (see [”
PROPER ACTIONS OF WREATH PRODUCTS AND GENERALIZATIONS (2009, methodology): “We also refer to [ CSV ] for applications of the result in harmonic analysis.”
On a class of $\mathrm{II}_1$ factors with at most one Cartan subalgebra (2007, result): “1 (by 2.11 above), the direct product L Γ of inﬁnitely many copies of Γ is not weakly amenable, i.e. Λcb( L Γ) = ∞. It is plausible that Γ itself is not weakly amenable. De Cornulier–Stalder–Valette ([CSV]) recently proved the surprising result that, despite satisfying Λcb(Γ) >1, the group Γ (and”
One-cohomology and the uniqueness of the group measure space decomposition of a II1 factor (2010, methodology): “ solidity of the free group factors LFn using the malleable deformation coming from the word length. Our proof is very close to Popa’s, replacing the word length by a proper 1-cocycle. It is shown in [CSV07] that for every ﬁnite group Hand n≥ 2, the wreath product Γ = H≀Fn := H(Fn)⋊F n admits a so-c”
Embeddings of Discrete Groups and the Speed of Random Walks (2007, methodology): “We refer to the papers [20, 11, 3, 14, 37, 2, 36, 13] and the references therein for background on this topic and several interesting applicati ons.”