Handle moves in contact surgery diagrams

TL;DR

This paper introduces handle moves in contact surgery diagrams, including contact Kirby moves, and applies them to classify long and loose Legendrian knots.

Contribution

It presents new handle move techniques in contact surgery diagrams and applies these to classify Legendrian knots.

Findings

Established contact Kirby moves.

Classified long Legendrian knots.

Classified loose Legendrian knots.

Abstract

We describe various handle moves in contact surgery diagrams, notably contact analogues of the Kirby moves. As an application of these handle moves, we discuss the respective classifications of long and loose Legendrian knots.