Distance of Heegaard splittings of knot complements

Maggy Tomova

Vol. 236 (2008), No. 1, 119–138

DOI: 10.2140/pjm.2008.236.119

Abstract

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 and let N(K) denote a regular neighborhood of K. Then either d(P) ≤ 2 − χ(Q − N(K)), or K can be isotoped to be disjoint from Q so that after the isotopy Q is a Heegaard surface for M − N(K) that is isotopic to a possibly stabilized copy of P.

Keywords

knot distance, bridge surface, Heegaard splitting

Mathematical Subject Classification 2000

Primary: 57M25, 57M27, 57M50

Milestones

Received: 18 May 2007

Accepted: 25 February 2008

Published: 1 May 2008