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

Primary: 57M27

Secondary: 57Q10

References

Forward citations

Publication

Received: 27 January 2005
Revised: 9 June 2005
Accepted: 8 November 2005
Published: 24 November 2005

Authors