On A Potential Contact Analogue Of Kirby Move Of Type 1

Abstract

In this 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 prove that no other contact integral surgery diagram satisfies those conditions except for contact $(+2)$-surgery on Legendrian unknot with Thruston--Bennequin number $-1$.