5 problems

Let $\Delta$ be an orientable simplicial $\Bbbk$-homology $d$-manifold without boundary, and let…

Let $\Delta$ be a balanced, orientable $\mathbf{k}$-homology manifold without boundary. Define $g”_j(\Delta)=h”_j(\Delta)-h”_{j-1}(\Delta)$. Balanced manifold $g”$-conjecture. The…

Let $\Delta$ be a homology manifold, let $h'_i$ denote its h-prime vector, and let $\beta_{i-1}$ denote its $(i-1)$st Betti number. Manifold g-conjecture. For every…

Let $\Delta$ be a homology manifold, and let $L^i_s(\Delta)$ denote the set of pairs consisting of a linear system of parameters and a one-form satisfying the partial Lefschetz con…

Let $\Delta$ be a homology sphere. Let $k[\Delta]$ be its Stanley–Reisner ring, let $\Theta$ be a linear system of parameters, and define $L(\Delta)$ to be the set of pairs…