L-space surgeries on links

An L -space link is a link in S^3 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 Manolescu and Ozsváth. 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.