4 problems

Let $\Delta_{m,n}$ be a chessboard complex with $n\geq m\geq 1$, and let $S/{\mathcal F}(\Delta_{m,n})$ denote its facet ring. Regularity-depth equality conjecture. … The preceding…

Freeness conjecture. The reduced homology group $\widetilde H_i(M_{m,n})$ is free if and only if $i\geq m-2$.

Let … -complex, with vertex set the pinched braids having precisely one regular strand. Sphericality conjecture. … is large enough. The paper presents this as evidence toward under…

Let $\mathsf{M}_{m,n}$ denote the chessboard complex, and let $\tilde{H}_{d}(\mathsf{M}_{m,n};\mathbb{Z})$ be its reduced homology. For the parametrization used in the source, let…