2014/09/30 by Yajing Liu · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Alexander polynomial #Combinatorics #Computer science #Floer homology #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Knot (papermaking) #Knot theory #Lens space #Link (geometry) #Mathematics #Pure mathematics #Space (punctuation) #math.GT #msc:57M25 #msc:57R58 #msc:57R65
paper · pdf · doi:10.4171/qt/96
published as Quantum Topology, Volume 8, Issue 3, 2017 · Section 2.4 deleted, proofs of Lemma 2.5, Theorem 3.8, and Theorem 1.15 adapted (which include the proof of Lemma 2.4, Lemma 3.9, and Theorem 3.10), and other various revisions
arxiv created 2015/04/23 · openalex publication_date 2017/08/22 · arxiv updated 2020/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 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.