Volume 5, issue 4 (2005)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Locally unknotted spines of Heegaard splittings

Jesse Johnson

Algebraic & Geometric Topology 5 (2005) 1573–1584

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