2 problems

Let $M_i$ ($i=1,2$) be irreducible 3-manifolds with connected boundary, with $\partial M_1\cong\partial M_2\cong F$. Let $\mathcal{D}_i$ be the set of essential curves in $F$ that…

Let $\M_g$ be moduli space with the Teichmüller metric, and let ${\cal C}_g$ be the curve complex of a closed genus-$g$ surface: its vertices are nontrivial, nonperipheral isotopy…