L‐space surgeries on 2‐component L‐space links

Abstract

In this paper, we analyze L‐space surgeries on two component L‐space links. We show that if one surgery coefficient is negative for the L‐space surgery, then the corresponding link component is an unknot. If the link admits a very negative (that is, d1,d2≪0 ) L‐space surgery, it is either the unlink or the Hopf link. We also give a way to characterize the torus link T(2,2l) by observing an L‐space surgery Sd1,d23(L) with some d1d2<0 on a 2‐component L‐space link with unknotted components. For some 2‐component L‐space links, we give explicit descriptions of the L‐space surgery sets.