Computing the Teichmueller polynomial

TL;DR

This paper introduces an algorithm to compute the Teichmueller polynomial for fibered 3-manifolds, aiding in understanding mapping classes with minimal stretch factors and fiber topology.

Contribution

The paper presents a novel algorithm for computing the Teichmueller polynomial associated with pseudo-Anosov mapping classes of disc homeomorphisms.

Findings

Algorithm efficiently computes the Teichmueller polynomial.

Enables derivation of fiber topology information.

Facilitates analysis of mapping classes with small stretch factors.

Abstract

The Teichmueller polynomial of a fibered 3-manifold plays a useful role in the construction of mapping class having small stretch factor. We provide an algorithm that computes this polynomial of the fibered face associated to a pseudo-Anosov mapping class of a disc homeomorphism. As a byproduct, our algorithm allows us to derive all the relevant informations on the topology of the different fibers that belong to the fibered face.