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 Knots with arbitrarily high distance bridge decompositions Bull. Korean Math. Soc. 2013 Vol. 50, No. 6, 1989-2000 https://doi.org/10.4134/BKMS.2013.50.6.1989Published online November 1, 2013 Kazuhiro Ichihara and Toshio Saito Nihon University, Joetsu University of Education Abstract : 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 Downloads: Full-text PDF