4 problems

Let $M^n_1$ and $M^n_2$ be two closed orientable $n$-manifolds. The regular genus additivity conjecture. … Regular genus is known to be subadditive under connected sum, and the equ…

Let $n$ be an integer with $n\geq 5$, and let $\Gamma^\prime$ be the $(n+1)$-regular colored graph constructed from the colored triangulation described in the paper. It has…

Let $M$ and $N$ be closed simply-connected PL $4$-manifolds, and let $\mathcal{G}(M)$ denote the graph-defined PL invariant regular genus of $M$. Ferri–Gagliardi–Grasselli's conjec…

Let $M$ be a closed connected prime orientable PL $4$-manifold, and let $\mathcal{G}(M)$ denote its regular genus. Spaggiari's conjecture. If $\mathcal{G}(M)=6$, then $M$ is topolo…