Detecting right-veering diffeomorphisms

TL;DR

This paper introduces a combinatorial method and algorithm to detect right-veering properties in open books, which are crucial for understanding tight contact structures in 3-manifolds.

Contribution

It provides a new combinatorial approach and an algorithm for identifying right-veering diffeomorphisms in open books, advancing the study of contact topology.

Findings

Developed a combinatorial criterion for left-veering arcs

Established an algorithm to detect right-veering property

Implications for classifying tight contact structures

Abstract

A result of Honda, Kazez, and Mati\'{c} states that a contact structure is tight if and only if all its supporting open books are right-veering. We show a combinatorial way of detecting the left-veering arcs in open books, implying the existence of an algorithm that detects the right-veering property for compact surfaces with boundary.