Mathematics > Geometric Topology
[Submitted on 15 Mar 2007 (v1), last revised 10 May 2007 (this version, v2)]
Title:Distance of Heegaard splittings of knot complements
View PDFAbstract: Let K be a knot in a closed orientable irreducible 3-manifold M and let P be a Heegaard splitting of the knot complement of genus at least two. Suppose Q is a bridge surface for K. Then either \begin{itemize} \item $d(P)\leq 2-\chi(Q-K)$, or \item K can be isotoped to be disjoint from Q so that after the isotopy Q is a Heegaard surface for the knot exterior and is isotopic to a possibly stabilized copy of P. \end{itemize}
Submission history
From: Maggy Tomova [view email][v1] Thu, 15 Mar 2007 22:41:49 UTC (55 KB)
[v2] Thu, 10 May 2007 19:27:36 UTC (57 KB)
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