Factorizations of diffeomorphisms of compact surfaces with boundary

TL;DR

This paper investigates the properties of surface diffeomorphisms, distinguishing those with positive Dehn twist factorizations from right veering ones, and constructs Stein-fillable 3-manifolds with monodromies lacking positive factorizations.

Contribution

It introduces methods to differentiate diffeomorphisms based on their factorizations and constructs examples of Stein-fillable 3-manifolds with monodromies without positive factorizations.

Findings

Identified criteria distinguishing positive factorizations from right veering diffeomorphisms.

Constructed open book decompositions with monodromies that have no positive factorization.

Provided new examples of Stein-fillable 3-manifolds with specific monodromy properties.

Abstract

We study diffeomorphisms of compact, oriented surfaces, developing methods of distinguishing those which have positive factorizations into Dehn twists from those which satisfy the weaker condition of right veering. We use these to construct open book decompositions of Stein-fillable 3-manifolds whose monodromies have no positive factorization.