L-SPACE SURGERIES ON LINKS

Abstract. An L-space link is a link in S3 on which all large surgeries are L-spaces. In this paper, we initiate a general study of the definitions, properties, and examples of L-space links. In particular, we find many hyperbolic L-space links, including some chain links and two-bridge links; from them, we obtain many hyperbolic L-spaces by integral surgeries, including the Weeks manifold. We give bounds on the ranks of the link Floer homology of L-space links and on the coefficients in the multi-variable Alexander polynomials. We also describe the Floer homology of surgeries on any L-space link using the link surgery formula of Ozsváth and Manolescu. As applications, we compute the graded Heegaard Floer homology of surgeries on 2-component L-space links in terms of only the Alexander polynomial and the surgery framing, and give a fast algorithm to classify L-space surgeries among them. 1