Distance of Heegaard splittings of knot complements

Details Distance of Heegaard splittings of knot complements Distance of Heegaard splittings of knot complements

2007-03-15

arxiv.org/abs/math/0703474v2

Mathematics

Geometric Topology

References added, exposition slightly improved, 17 pages, 3 figures

Scientific paper

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}

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