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Polynomial-time algorithms for the curve graph

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arxiv 1609.09392 v2 pith:TNJ3MKD7 submitted 2016-09-29 math.GT

Mark C. Bell , Richard C. H. Webb This is my paper · ORCID
classification math.GT
keywords computecurvecurvesgraphlengthmappingpolynomial-timealgorithm
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We describe a polynomial-time algorithm to compute a (tight) geodesic between two curves in the curve graph. As well as enabling us to compute the distance between a pair of curves, this has several applications to mapping classes. For example, we can use these geodesics to compute the asymptotic translation length, Nielsen--Thurston type, and canonical curve system of a mapping class in polynomial time in its word length.

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  1. On Translation Lengths of Anosov Maps on Curve Graph of Torus

    math.GT 2019-08 conditional novelty 5.0 of 10

    Every Anosov map of the torus has a bi-infinite geodesic axis in the Farey graph, making its stable translation length a computable positive integer.

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