Algebraic & Geometric Topology

Heegaard splittings and the pants complex

Jesse Johnson

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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.

Article information

Source
Algebr. Geom. Topol., Volume 6, Number 2 (2006), 853-874.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796547

Digital Object Identifier
doi:10.2140/agt.2006.6.853

Mathematical Reviews number (MathSciNet)
MR2240918

Zentralblatt MATH identifier
1130.57029

Subjects
Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx]
Secondary: 57M27: Invariants of knots and 3-manifolds 57M99: None of the above, but in this section

Keywords
Heegaard splitting curve complex pants complex

Citation

Johnson, Jesse. Heegaard splittings and the pants complex. Algebr. Geom. Topol. 6 (2006), no. 2, 853--874. doi:10.2140/agt.2006.6.853. https://projecteuclid.org/euclid.agt/1513796547


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References

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