Volume 6, issue 2 (2006)

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Heegaard splittings and the pants complex

Jesse Johnson

Algebraic & Geometric Topology 6 (2006) 853–874

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