6 problems

Let $M_f$ be a hyperbolic $3$-manifold with Heegaard surface $\Sigma$ of minimal genus, and let ${\mathcal D}_1$ and ${\mathcal D}_2$ be the disk sets of the two handlebodies. For…

Let $\Sigma_{1}$ and $\Sigma_{2}$ be compact, orientable surfaces, and let $\mathcal{P}(\Sigma)$ denote the pants graph of a surface $\Sigma$. A subgraph is totally geodesic if eve…

Let $M_f$ be a closed hyperbolic $3$-manifold with Heegaard surface … between a pants decomposition consisting of pants curves in ${\mathcal D}_1$ and one consisting of pants curve…

Let $\Sigma'$ and $\Sigma$ be surfaces, and let $\mathcal{P}(\Sigma)$ denote the pants graph of $\Sigma$. Suppose that … is an injective simplicial map. Aramayona–Parlier–Shackleto…

Let $\Sigma_{1}$ and $\Sigma_{2}$ be compact, orientable surfaces, and let $\mathcal{P}(\Sigma_i)$ denote the pants graph of $\Sigma_i$. A simplicial embedding is a map … that pres…

All-strata total-geodesicity conjecture. Every stratum $\mathcal P_C(S)$ is totally geodesic in $\mathcal P(S)$.