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Mathematics  2004 

Locally unknotted spines of Heegaard splittings

DOI: 10.2140/agt.2005.5.1573

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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.


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