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, d 1 , d 2 ≪ 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 , 2 l ) by observing an L-space surgery S d 1 , d 2 3 ( L ) with some d 1 d 2 < 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.
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