2 problems

Let $M$ be a closed, irreducible $3$-manifold and let $\mathcal F$ be a maximal embedded collection of orientable, incompressible surfaces. If $M-N(\mathcal F)$ has $n$ components,…

Let $M$ be a compact $3$-manifold and let $T$ be a separating, incompressible, orientable surface of genus $g$ properly embedded in $M$. If $M_1$ and $M_2$ are the components of…