Knots with arbitrarily high distance bridge decompositions
Bull. Korean Math. Soc. 2013 Vol. 50, No. 6, 1989-2000
https://doi.org/10.4134/BKMS.2013.50.6.1989
Published 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
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