Bulletin of the
Korean Mathematical Society BKMS

We show that for any given closed orientable 3-manifold $M$ with a Heegaard surface of genus $g$, any positive integers $b$ and $n$, there exists a knot $K$ in $M$ which admits a $(g,b)$-bridge splitting of distance greater than $n$ with respect to the Heegaard surface except for $(g,b)=(0,1), (0,2)$.

Keywords: knot, Heegaard splitting, bridge decomposition, distance

MSC numbers: Primary 57M50; Secondary 57M25