Locally unknotted spines of Heegaard splittings

Johnson, Jesse

doi:10.2140/agt.2005.5.1573

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Locally unknotted spines of Heegaard splittings

Jesse Johnson

Algebraic & Geometric Topology 5 (2005) 1573–1584

DOI: 10.2140/agt.2005.5.1573

arXiv: math.GT/0411065

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

Mathematical Subject Classification 2000

Primary: 57M27

Secondary: 57Q10

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Publication

Received: 27 January 2005

Revised: 9 June 2005

Accepted: 8 November 2005

Published: 24 November 2005

Authors

Jesse Johnson
Mathematics Department University of California Davis CA 95616 USA

Volume 5, issue 4 (2005)