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The Connectivity of Multicurves Determined by Integral Weight Train Tracks
Andrew Haas and Perry Susskind
Transactions of the American Mathematical Society
Vol. 329, No. 2 (Feb., 1992), pp. 637-652
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2153956
Page Count: 16
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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.
Transactions of the American Mathematical Society © 1992 American Mathematical Society