On A Potential Contact Analogue Of Kirby Move Of Type 1

TL;DR

This paper investigates the potential existence of a contact analogue of Kirby move of type 1, identifying conditions on contact surgery diagrams that could enable such moves, and highlighting specific diagrams that meet these conditions.

Contribution

It introduces necessary conditions for contact Kirby move of type 1 and identifies candidate diagrams satisfying these conditions.

Findings

Certain contact positive integral surgery diagrams on Legendrian unknots meet the conditions for a potential contact Kirby move of type 1.

The paper provides a framework to identify diagrams that could admit contact Kirby moves of type 1.

It opens avenues for further exploration of contact Kirby calculus and surgery techniques.

Abstract

In this expository note, we explore the possibility of the existence of Kirby move of type 1 for contact surgery diagrams. In particular, we give the necessary conditions on a contact surgery diagram to become a potential candidate for contact Kirby move of type 1. We observe that there is a collection of contact positive integral surgery diagrams on Legendrian unknots satisfying those conditions.