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Polynomial invariants of pseudo-Anosov maps
Journal article   Open access   Peer reviewed

Polynomial invariants of pseudo-Anosov maps

Joan Birman, Peter Brinkmann and Keiko Kawamuro
Journal of topology and analysis, Vol.4(1), pp.13-47
01/27/2010
DOI: 10.1142/S1793525312500033

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Abstract

Journal of Topology and Analysis, Vol. 4, No 1 (2012) 13-47 We investigate the structure of the characteristic polynomial det(xI-T) of a transition matrix T that is associated to a train track representative of a pseudo-Anosov map [F] acting on a surface. As a result we obtain three new polynomial invariants of [F], one of them being the product of the other two, and all three being divisors of det(xI-T). The degrees of the new polynomials are invariants of [F ] and we give simple formulas for computing them by a counting argument from an invariant train track. We give examples of genus 2 pseudo-Anosov maps having the same dilatation, and use our invariants to distinguish them.
Mathematics - Geometric Topology

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