Geodesic
Stabilizing Heegaard splittings of high-distance knots
Mossessian, George1
1Department of Mathematics, University of California, Davis, 1 Shields Avenue, Davis, CA 95616, United States
Algebraic and Geometric Topology, Tome 16 (2016) no. 6, pp. 3419-3443
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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.

DOI : 10.2140/agt.2016.16.3419
Classification : 57M25, 57M27
Keywords: knot complement, high distance, common stabilization, Heegaard splitting, tunnel system

Mossessian, George  1

1 Department of Mathematics, University of California, Davis, 1 Shields Avenue, Davis, CA 95616, United States 
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Mossessian, George. Stabilizing Heegaard splittings of high-distance knots. Algebraic and Geometric Topology, Tome 16 (2016) no. 6, pp. 3419-3443. doi: 10.2140/agt.2016.16.3419

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