English

Knots with arbitrarily high distance bridge decompositions

Geometric Topology 2013-08-01 v4

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

Cite

@article{arxiv.1209.0097,
  title  = {Knots with arbitrarily high distance bridge decompositions},
  author = {Kazuhiro Ichihara and Toshio Saito},
  journal= {arXiv preprint arXiv:1209.0097},
  year   = {2013}
}

Comments

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

R2 v1 2026-06-21T21:58:25.307Z