LL-space surgeries on links

  • Yajing Liu

    University of California, Los Angeles, USA
$L$-space surgeries on links cover
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An LL-space link is a link in S3S^3 on which all large surgeries are LL-spaces. In this paper, we initiate a general study of the definitions, properties, and examples of LL-space links. In particular, we find many hyperbolic LL-space links, including some chain links and two-bridge links; from them, we obtain many hyperbolic LL-spaces by integral surgeries, including the Weeks manifold. We give bounds on the ranks of the link Floer homology of LL-space links and on the coefficients in the multi-variable Alexander polynomials. We also describe the Floer homology of surgeries on any LL-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 LL-space links in terms of only the Alexander polynomial and the surgery framing, and give a fast algorithm to classify LL-space surgeries among them.

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Yajing Liu, LL-space surgeries on links. Quantum Topol. 8 (2017), no. 3, pp. 505–570

DOI 10.4171/QT/96