Polynomial invariants of pseudo-Anosov maps

Joan Birman; Peter Brinkmann; Keiko Kawamuro

doi:10.1142/s1793525312500033

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arXiv · 1001.5094

Polynomial invariants of pseudo-Anosov maps

Joan Birman·Peter Brinkmann·Keiko Kawamuro

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Abstract

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.

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BibTeX RIS

Joan Birman, Peter Brinkmann, Keiko Kawamuro. 2012-04-18. Polynomial invariants of pseudo-Anosov maps. https://doi.org/10.1142/s1793525312500033

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