4 problems

Matveev's lens-space complexity conjecture. The Matveev complexity of $L(2n+1,n)$ is

Let $M$ be a torus bundle over $S^1$ with monodromy $A\in\operatorname{GL}_2(\mathbb{Z})$, and let $\|A\|$ denote the norm used in the source. Anisov's conjecture. The complexity o…

Let $M$ be one of the manifolds considered in Sections 2.3 and 2.4, and let $P$ be the corresponding spine constructed there. If $P$ has $k$ vertices, then minimality conjecture.…

Let $M$ be a compact connected orientable $3$-manifold. The Matveev complexity $c(M)$ and the modified Heegaard complexity $\widetilde{c}(M)$ are defined by minimizing the correspo…