An -space link is a link in on which all large surgeries are -spaces. In this paper, we initiate a general study of the definitions, properties, and examples of -space links. In particular, we find many hyperbolic -space links, including some chain links and two-bridge links; from them, we obtain many hyperbolic -spaces by integral surgeries, including the Weeks manifold. We give bounds on the ranks of the link Floer homology of -space links and on the coefficients in the multi-variable Alexander polynomials. We also describe the Floer homology of surgeries on any -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 -space links in terms of only the Alexander polynomial and the surgery framing, and give a fast algorithm to classify -space surgeries among them.
Cite this article
Yajing Liu, -space surgeries on links. Quantum Topol. 8 (2017), no. 3, pp. 505–570DOI 10.4171/QT/96