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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The connectivity of multicurves determined by integral weight train tracks


Authors: Andrew Haas and Perry Susskind
Journal: Trans. Amer. Math. Soc. 329 (1992), 637-652
MSC: Primary 57N05
MathSciNet review: 1028309
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Abstract: An integral weighted train track on a surface determines the isotopy class of an embedded closed $ 1$-manifold. We are interested in the connectivity of the resulting $ 1$-manifold. In general there is an algorithm for determining connectivity, and in the simplest case of a $ 2$-parameter train track on a surface of genus one there is an explicit formula. We derive a formula for the connectivity of the closed $ 1$-manifold determined by a $ 4$-parameter train track on a surface of genus two which is computable in polynomial time. We also give necessary and sufficient conditions on the parameters for the resulting $ 1$-manifold to be connected.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1028309-1
PII: S 0002-9947(1992)1028309-1
Keywords: Train track, surface topology, multiple curves
Article copyright: © Copyright 1992 American Mathematical Society