Knots with arbitrarily high distance bridge decompositions
arXiv:1209.0097
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).
10 pages, 1 figure: v2, some inaccurate statements (including Abstract and Main Theorem) corrected, acknowledgements and remarks added: v3&v4, typos are corrected, arguments are simplified, incorporation of referee comments. To appear in Bull. Korean Math. Soc