Algebraic and Geometric Topology 5 (2005), paper no. 63, pages 1573-1584.

Locally unknotted spines of Heegaard splittings

Jesse Johnson

Abstract. We show that under reasonable conditions, the spines of the handlebodies of a strongly irreducible Heegaard splitting will intersect a closed ball in a graph which is isotopic into the boundary of the ball. This is in some sense a generalization of the results by Scharlemann on how a strongly irreducible Heegaard splitting surface can intersect a ball.

Keywords. Heegaard splitting, sweep-out, locally unkotted spine

AMS subject classification. Primary: 57M27. Secondary: 57Q10.

E-print: arXiv:math.GT/0411065

DOI: 10.2140/agt.2005.5.1573

Submitted: 27 January 2005. (Revised: 9 June 2005.) Accepted: 8 November 2005. Published: 24 November 2005.

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Jesse Johnson
Mathematics Department, University of California
Davis, CA 95616, USA

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