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2006 Heegaard splittings and the pants complex
Jesse Johnson
Algebr. Geom. Topol. 6(2): 853-874 (2006). DOI: 10.2140/agt.2006.6.853

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.

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Jesse Johnson. "Heegaard splittings and the pants complex." Algebr. Geom. Topol. 6 (2) 853 - 874, 2006. https://doi.org/10.2140/agt.2006.6.853

Information

Received: 5 May 2006; Accepted: 11 May 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1130.57029
MathSciNet: MR2240918
Digital Object Identifier: 10.2140/agt.2006.6.853

Subjects:
Primary: 57N10
Secondary: 57M27, 57M99

Rights: Copyright © 2006 Mathematical Sciences Publishers

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