Additivity of Heegaard genera of bounded surface sums

Ruifeng Qiu, Shicheng Wang, Mingxing Zhang

Let $M$ be a surface sum of 3-manifolds $M_1$ and $M_2$ along a bounded connected surface $F$ and ${\partial }_i$ be the component of $\partial M_i$ containing $F$. If $M_i$ has a hig…