POLYNOMIAL INVARIANTS OF PSEUDO-ANOSOV MAPS-Reference-Cited by-同舟云学术

POLYNOMIAL INVARIANTS OF PSEUDO-ANOSOV MAPS

Published:2012-03 Issue:01 Volume:04 Page:13-47
ISSN:1793-5253
Container-title:Journal of Topology and Analysis
language:en
Short-container-title:J. Topol. Anal.

Author:

BIRMAN JOAN¹,BRINKMANN PETER²,KAWAMURO KEIKO³

Affiliation:

1. Department of Mathematics, Columbia University, 2990 Broadway, New York City, NY 10027, USA

2. Google Inc., USA

3. Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, IA 52242, USA

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Geometry and Topology,Analysis

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793525312500033

Reference10 articles.

1. Train-tracks for surface homeomorphisms

2. An Implementation of the Bestvina–Handel Algorithm for Surface Homeomorphisms

3. A Primer on Mapping Class Groups

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