This is an announcement for the paper "Relatively expanding box spaces with no expansion" by Goulnara Arzhantseva and Romain Tessera.

Abstract: We exhibit a finitely generated group $G$ and a sequence of finite index normal subgroups $N_n\trianglelefteq G$ such that for every finite generating subset $S\subseteq G$, the sequence of finite Cayley graphs $(G/N_n, S)$ does not coarsely embed into any $L^p$-space for $1\leqslant p<\infty$ (moreover, into any uniformly curved Banach space), and yet admits no weakly embedded expander.

Archive classification: math.GR math.FA math.MG

Mathematics Subject Classification: 46B85, 20F69, 22D10, 20E22

Remarks: 20 pages

Submitted from: goulnara.arjantseva@univie.ac.at

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1402.1481

or

http://arXiv.org/abs/1402.1481