Heegaard splittings and the pants complex

Details Heegaard splittings and the pants complex Heegaard splittings and the pants complex

2005-09-28

arxiv.org/abs/math/0509680v2

Algebr. Geom. Topol. 6 (2006) 853-874

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 11 July 2006

Scientific paper

10.2140/agt.2006.6.853

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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