2 problems

The three-dimensional case of Lutz and Nevo's conjecture. For every flag triangulation $T$ of $S^3$ with $\gamma_2(T)=0$, there is a sequence of such collapses that reduces $T$ to…

Uniqueness conjecture. $T_{12}$ is, up to isomorphism, the only flag triangulation of $S^3$ with 12 vertices in which every edge is contained in a square.