15 problems

Let $X$ have a single boundary component $F$ with $g(F)\geq 2$, and let $V\cup_H W$ be a minimal-genus Heegaard splitting of $X$ with $F$ contained in the compression body $V$. Let…

For a set of minima, let $C_{\mathrm{max}}$ be the largest set of curves containing $C$ for which every nonfilling subset $C'$ of $C_{\mathrm{max}}$ gives…

Let $\Gamma$ be a finite-index subgroup of $\operatorname{Mcg}(\Sigma)$, and let $\alpha$ be a simple closed curve on $\Sigma$. A subgroup of $\operatorname{Mcg}(\Sigma)$ is congru…

Let $S_{g,n}$ be a genus-$g$ surface with $n$ punctures, let $\Mod(S_{g,n})$ be its mapping class group, let $\PMod(S_{g,n})$ be the pure mapping class group, and let $L_{\C}(G)$ d…

Let $\gamma$ be a Teichmüller geodesic with endpoints $\gamma^-$ and $\gamma^+$ in the Thurston boundary, and call it sticky when it satisfies the sticky-geodesic condition that ge…

Let $\Sigma$ be a surface, let $\mathcal{C}_R(\Sigma)$ be a complex of regions, and let $N$ be a normal subgroup of $\operatorname{Map}^{\pm}(\Sigma)$. Brendle–Margalit conjectures…

Let $S_g$ be a closed orientable surface and let $\mathcal C_A(S_g)$ be a complex of regions associated to $S_g$. Assume that $\mathcal C_A(S_g)$ is connected and admits no exchang…

Let $S_g$ be a closed surface of genus $g$, and let $\mathcal C_A(S_g)$ be a complex of regions that is connected and has no holes or corks. Complex-of-regions conjecture. The natu…

Let $K$ be a knot in a 3-manifold $M$ with a $(g,b)$-splitting, where $g\geq 1$. Let $(g',b',n)$ be a triple of non-negative integers with $g'\geq g$ and $b'\geq b$. High-distance…

Electric-model quasi-isometry conjecture. The map $\varphi$ is a quasi-isometry.

Short Curve conjecture. If $g$ is a Weil–Petersson geodesic with end invariant $(\nu^{-},\nu^{+})$, then:

Let $S$ be a finite-type surface. Let $\mathcal{C} (S)_{\operatorname{sub}}$ be the subspace model of the curve complex, and let…

Let $S$ be a $p$-punctured surface of genus $g$. Write $\mathcal{C} (S)$ for its curve complex, $\mathcal{E} \mathcal{L} (S)$ for its ending lamination space, and…

Let $S_{g,n}$ be a surface of genus $g$ with $n$ punctures, let $\operatorname{Mod}(S_{g,n})$ be its mapping class group, and let $L_{\mathcal C}(\operatorname{Mod}(S_{g,n}))$ deno…

Nontriviality conjecture. For $g \geq 1$, the class