Heegaard splittings and the pants complex

Johnson, Jesse

doi:10.2140/agt.2006.6.853

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Heegaard splittings and the pants complex

Jesse Johnson

Algebraic & Geometric Topology 6 (2006) 853–874

DOI: 10.2140/agt.2006.6.853

arXiv: math.GT/0509680

Abstract

We define integral measures of complexity for Heegaard splittings based on the graph dual to the curve complex and on the pants complex defined by Hatcher and Thurston. As the Heegaard splitting is stabilized, the sequence of complexities turns out to converge to a non-trivial limit depending only on the manifold. We then use a similar method to compare different manifolds, defining a distance which converges under stabilization to an integer related to Dehn surgeries between the two manifolds.

Keywords

Heegaard splitting, curve complex, pants complex

Mathematical Subject Classification 2000

Primary: 57N10

Secondary: 57M27, 57M99

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Publication

Received: 5 May 2006

Accepted: 11 May 2006

Published: 11 July 2006

Authors

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

Volume 6, issue 2 (2006)