The Heegaard distances cover all non-negative integers

Ruifeng Qiu, Yanqing Zou, Qilong Guo

In this paper, we prove that (1) For any integers $n\ge 1$ and $g\ge 2$, there is a closed 3-manifold $M_g^n$ which admits a distance $n$ Heegaard splitting of genus $g$ exce…