5 problems

A triangulation $\mathcal{T}$ is a finite triangulation of a closed 3-manifold, and $S^3$ recognition asks whether $\mathcal{T}$ triangulates the 3-sphere. The complexity class…

For each $n$, let $\overline{\sigma}_n$ denote the average number of vertex normal surfaces over all closed 3-manifold triangulations of size $n$, counted up to isomorphism. A vert…

Let $n$ be a positive integer other than $1,2,3,5$, and let $k$ be the integer determined by the congruence class of $n$ modulo $4$. A vertex normal surface is a vertex solution in…

Fibonacci-growth conjecture. For every $n\geq 3$, the mean admissible vertex count satisfies

Tight upper-bound conjecture. For every positive $n\neq 1,2,3,5$, equation gives a tight upper bound on the admissible vertex count $\sigma$. Consequently,