Reducible and $\partial $-reducible handle additions
Reducible and $\partial $-reducible handle additions
Let $M$ be a simple 3-manifold with $F$ a component of $\partial M$ of genus at least two. For a slope $\alpha$ on $F$, we denote by $M(\alpha )$ the manifold obtained by attaching a 2-handle to $M$ along a regular neighborhood of $\alpha$ on $F$. Suppose that $\alpha$ and …