Stabilizing the monodromy of an open book decomposition

TL;DR

This paper demonstrates that any mapping class on a compact oriented surface with boundary can be transformed into a pseudo-Anosov, right-veering class through positive stabilizations, aiding in the understanding of surface automorphisms.

Contribution

It introduces a method to stabilize any boundary surface mapping class to achieve pseudo-Anosov and right-veering properties, expanding the toolkit for studying surface automorphisms.

Findings

Any boundary mapping class can be stabilized to become pseudo-Anosov.

Positive stabilizations can ensure right-veering behavior.

The method applies to all surfaces with nonempty boundary.

Abstract

We prove that any mapping class on a compact oriented surface with nonempty boundary can be made pseudo-Anosov and right-veering after a sequence of positive stabilizations.