4 problems

Stable compressed-rank conjecture. For every Stallings graph $\Gamma$ and $d\in\mathbb{N}$,

For a $k$-complex $X$, define its ${\mathbb Z}$-rank $r_{\mathbb Z}(X)$ to be the minimum of $\operatorname{rk}\cap_{N,{\mathbb Z}}$ over all $(k-1)$-connected PL $2k$-manifolds…

Agreement of ranks conjecture. For low $U$-rank representations, these inequalities should be replaced by equalities. Thus all three rank notions coincide on low $U$-rank represent…

For a representation $\rho$ of $GL_n$ or $Sp_{2n}$ having low $U$-rank, write $rank_U(\rho)$ for its $U$-rank and $rank_{\otimes}(\rho)$ for its tensor rank. Agreement of ranks con…