Polynomial invariants of pseudo-Anosov maps
Geometric Topology
2012-04-20 v7
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.
Keywords
Cite
@article{arxiv.1001.5094,
title = {Polynomial invariants of pseudo-Anosov maps},
author = {Joan Birman and Peter Brinkmann and Keiko Kawamuro},
journal= {arXiv preprint arXiv:1001.5094},
year = {2012}
}
Comments
Published in Journal of Topology and Analysis, Vol. 4, No 1 (2012) 13-47