High-dimensional expansion and soficity of groups

Abstract

For $d\ge 4$ and $p$ a sufficiently large prime, we construct a lattice $\hat{I}“\le {\mathrm{PSp}}_{2d}({\mathbb{Q}}_p),$ such that its universal central extension cannot be sofic if $\hat{I}“$ satisfies some weak form of stability in permutations. In the proof, we make use of high-dimensional expansion phenomena and, extending results of Lubotzky, we construct new examples of cosystolic expanders over arbitrary finite abelian groups.

23 pages, no figures; v2 update