2006/07/31 by Yair Minsky, Yoav Moriah, Saul Schleimer · 1 citation
Mathematics · #math.GT #msc:57M25
paper · pdf · doi:10.2140/agt.2007.7.1471
published as Algebr. Geom. Topol. 7 (2007) 1471-1483 · 13 pages, 3 figures. Added reference
arxiv created 2007/08/15 · arxiv updated 2014/09/30
We construct knots in S3 with Heegaard splittings of arbitrarily high distance, in any genus. As an application, for any positive integers t and b we find a tunnel number t knot in the three-sphere which has no (t,b)-decomposition.