Boundary reducible handle additions on simple 3-manifolds

Yannan Li, Ruifeng Qiu, Mingxing Zhang

Let $M$ be a simple manifold, and $F$ be a component of $\partial M$ of genus two. For a slope $\gamma$ on $F$, we denote by $M(\gamma )$ the manifold obtained by attaching a 2-handle to $M$…