L-space surgeries on 2-component L-space links

Abstract

In this paper, we analyze L-space surgeries on two component L-space links. We show that if one surgery coefficient is negative for the L-space surgery, then the corresponding link component is an unknot. If the link admits very negative (i.e. $d_1,d_2\ll 0$) L-space surgeries, it is the Hopf link. We also give a way to characterize the torus link $T(2,2l)$ by observing an L-space surgery $S_{d_1,d_2}^3(\mathcal{L})$ with $d_1{d}_2<0$ on a 2-component L-space link with unknotted components. For some 2-component L-space links, we give explicit descriptions of the L-space surgery sets.

arXiv comment28 pages

References in corpus (12)

• Holomorphic disks and genus bounds
• Holomorphic disks and link invariants
• Knot Floer homology and rational surgeries
• Heegaard Floer homology and integer surgeries on links
• $L$-space surgeries on links
• L-spaces, taut foliations, and graph manifolds
• L-space intervals for Graph Manifolds and Cables
• 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
• Fibered and strongly quasi-positive $L$-space links

Cited by in corpus (1)

• Knot Floer homology, link Floer homology and link detection