On the flux of pseudo-Anosov homeomorphisms

TL;DR

This paper presents a specific pseudo-Anosov homeomorphism that acts trivially on homology but has a non-zero flux, highlighting a nuanced property of surface homeomorphisms.

Contribution

It constructs an example of a pseudo-Anosov homeomorphism with trivial homological action yet non-zero flux, revealing new insights into surface dynamics.

Findings

Existence of a pseudo-Anosov with trivial homology action and non-zero flux

Demonstrates flux can be non-zero despite trivial homological action

Provides a counterexample to assumptions linking flux and homology

Abstract

We exhibit a pseudo-Anosov homeomorphism of a surface S which acts trivially on the first homology group of S and whose flux is non zero