3 problems

Let $\Gamma$ be an amenable group, let $\Sigma$ and $\Sigma'$ be two sofic approximations of $\Gamma$, and let $X$ be a uniformly bounded representation of $\Gamma$. Approximation-…

Let $2<p<\infty$, let $\Gamma$ be a countable discrete sofic group, and let $\Sigma$ be a sofic approximation of $\Gamma$. Equality conjecture. For every $n\in\mathbb N$, … This co…

Let $\Gamma$ be an amenable group and let $Y\subseteq l^{p}(\Gamma)^{\oplus n}$ for some $n\in \mathbb N$. Let $\dim_{l^{p}}^{G}(Y,\Gamma)$ denote the $l^{p}$-dimension defined by…