The connectivity of multicurves determined by integral weight train tracks
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- by Andrew Haas and Perry Susskind PDF
- Trans. Amer. Math. Soc. 329 (1992), 637-652 Request permission
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.References
- Andrew Haas and Perry Susskind, The geometry of the hyperelliptic involution in genus two, Proc. Amer. Math. Soc. 105 (1989), no. 1, 159–165. MR 930247, DOI 10.1090/S0002-9939-1989-0930247-2
- Robert C. Penner, An introduction to train tracks, Low-dimensional topology and Kleinian groups (Coventry/Durham, 1984) London Math. Soc. Lecture Note Ser., vol. 112, Cambridge Univ. Press, Cambridge, 1986, pp. 77–90. MR 903859 J. Harer and R. C. Penner, Combinatories of train tracks, unpublished manuscript. W. Thurston, The geometry and topology of $3$-manifolds, Princeton Univ. Notes.
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 329 (1992), 637-652
- MSC: Primary 57N05
- DOI: https://doi.org/10.1090/S0002-9947-1992-1028309-1
- MathSciNet review: 1028309