Pseudo-Anosov homeomorphisms not arising from branched covers

TL;DR

This paper investigates the relationship between the algebraic degree of stretch factors and surface genus for pseudo-Anosov homeomorphisms, providing a negative answer to a previously posed question.

Contribution

It demonstrates that not all pseudo-Anosov homeomorphisms with certain algebraic properties arise from branched covers, challenging existing assumptions.

Findings

Counterexamples to Farb's question about stretch factor degree and genus

Pseudo-Anosov homeomorphisms not derived from branched covers

Negative answer to the relation between algebraic degree and surface genus

Abstract

In this paper we provide a negative answer to a question of Farb about the relation between the algebraic degree of the stretch factor of a pseudo-Anosov homeomorphism and the genus of the surface on which it is defined.