4 problems

Neighborly sphere-product conjecture. There is a centrally $(\lfloor d/2\rfloor+1)$-neighborly combinatorial triangulation of every product…

Sparla's existence conjecture. There are centrally $(r+1)$-neighborly triangulations of $S^r\times S^r$ on $4r+4$ vertices.

Let $n$ and $m$ be positive integers. A continuous map is considered from the product of spheres $\mathbb{S}^n\times\mathbb{S}^m$ to $\mathbb{S}^{n+m}$, and $\binom{n+m}{n}$ denote…

Diffeomorphism conjecture. $\mathcal{Z}_{K}$ is diffeomorphic to the connected sum of sphere products in Proposition 1.