$L$-space surgeries on links

Abstract

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 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.

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

References in corpus (4)

• Knot Floer homology detects fibred knots
• On Floer homology and the Berge conjecture on knots admitting lens space surgeries
• Heegaard Floer homology of surgeries on two-bridge links
• An introduction to knot Floer homology

Cited by in corpus (9)

• Immersed concordances of links and Heegaard Floer homology
• Heegaard Floer homology of L-space links with two components
• Four genera of links and Heegaard Floer homology
• L-space surgeries on satellites by algebraic links
• L-spaces, taut foliations and the Whitehead link
• L-space surgeries on 2-component L-space links
• Fibered and strongly quasi-positive $L$-space links
• Chainmail links and L-spaces
• L-spaces, taut foliations and fibered hyperbolic two-bridge links