On A Potential Contact Analogue Of Kirby Move Of Type 1

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.