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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Stabilizing Heegaard splittings of high-distance knots

George Mossessian

Algebraic & Geometric Topology 16 (2016) 3419–3443
Abstract

Suppose K is a knot in S3 with bridge number n and bridge distance greater than 2n. We show that there are at most 2n n distinct minimal-genus Heegaard splittings of S3 η(K). These splittings can be divided into two families. Two splittings from the same family become equivalent after at most one stabilization. If K has bridge distance at least 4n, then two splittings from different families become equivalent only after n 1 stabilizations. Furthermore, we construct representatives of the isotopy classes of the minimal tunnel systems for K corresponding to these Heegaard surfaces.

Keywords
knot complement, high distance, common stabilization, Heegaard splitting, tunnel system
Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57M27
References
Publication
Received: 8 September 2015
Revised: 15 February 2016
Accepted: 21 April 2016
Published: 15 December 2016
Authors
George Mossessian
Department of Mathematics
University of California, Davis
1 Shields Avenue
Davis, CA 95616
United States
http://math.ucdavis.edu/~gmoss