Right-veering diffeomorphisms of compact surfaces with boundary I

TL;DR

This paper introduces the concept of right-veering diffeomorphisms on compact surfaces with boundary, exploring their algebraic structure and connections to contact geometry and open book decompositions.

Contribution

It initiates the study of the monoid of right-veering diffeomorphisms, showing it properly contains positive Dehn twists and relating it to contact structures.

Findings

The monoid of right-veering diffeomorphisms is strictly larger than positive Dehn twists.

Established connections between right-veering diffeomorphisms and tight contact structures.

Linked right-veering diffeomorphisms to open book decompositions.

Abstract

We initiate the study of the monoid of right-veering diffeomorphisms on a compact oriented surface with nonempty boundary. The monoid strictly contains the monoid of products of positive Dehn twists. We explain the relationship to tight contact structures and open book decompositions.