8 problems

Let $\Delta$ be an orientable $(d-1)$-dimensional $\mathbf{k}$-homology manifold without boundary. Define the modified $h$-numbers $h_i”$ as in the source by … where…

The centrally symmetric lower bound conjecture. If $\Delta$ is a simplicial sphere, a connected simplicial manifold, or a normal pseudomanifold, then

Let $\Delta$ be an arbitrary $(d-1)$-dimensional simplicial manifold with $n$ vertices, and let $\tilde{\beta}_r(\Delta)$ denote its reduced $r$-th Betti number. For…

Let $m\geq 2$, and let $\Delta$ be a flag homology $(2m-1)$-manifold with $n$ vertices. The Gal's stability conjecture. There exists a constant $b=b(m)$ such that if … then…

Symmetric infinitesimal rigidity conjecture. If $\Delta$ is a simplicial sphere, a connected simplicial manifold, or a normal pseudomanifold and $d-1\geq 3$, then there exists a sy…

Flag-manifold conjecture. Every flag simplicial manifold is pure-EKR.

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…

Bagchi's converse conjecture. If this equality holds, then $\Delta$ is locally $(r-1)$-stacked. The conjecture was verified for $3$-dimensional homology manifolds, but is otherwise…