## Algebraic & Geometric Topology

### Links of plane curve singularities are $L$–space links

#### Abstract

We prove that a sufficiently large surgery on any algebraic link is an $L$–space. For torus links we give a complete classification of integer surgery torus links we give a complete classification of integer surgery coefficients providing $L$–spaces.

#### Article information

Source
Algebr. Geom. Topol., Volume 16, Number 4 (2016), 1905-1912.

Dates
Revised: 26 September 2015
Accepted: 11 December 2015
First available in Project Euclid: 28 November 2017

https://projecteuclid.org/euclid.agt/1511895903

Digital Object Identifier
doi:10.2140/agt.2016.16.1905

Mathematical Reviews number (MathSciNet)
MR3546454

Zentralblatt MATH identifier
1364.14022

#### Citation

Gorsky, Eugene; Némethi, András. Links of plane curve singularities are $L$–space links. Algebr. Geom. Topol. 16 (2016), no. 4, 1905--1912. doi:10.2140/agt.2016.16.1905. https://projecteuclid.org/euclid.agt/1511895903

#### References

• M Artin, Some numerical criteria for contractability of curves on algebraic surfaces, Amer. J. Math. 84 (1962) 485–496
• M Artin, On isolated rational singularities of surfaces, Amer. J. Math. 88 (1966) 129–136
• E Gorsky, A Némethi, Lattice and Heegaard Floer homologies of algebraic links, Int. Math. Res. Not. 2015 (2015) 12737–12780
• E Gorsky, A Némethi, On the set of $L$–space surgeries for links, preprint (2015)
• R,L Graham, D,E Knuth, O Patashnik, Concrete mathematics: a foundation for computer science, 2nd edition, Addison-Wesley, Reading, MA (1994)
• J Hanselman, Computing $\widehat{\mathrm{HF}}$ of graph manifolds Python module Available at \setbox0\makeatletter\@url http://math.columbia.edu/~jhansel/graph_manifolds_program.html {\unhbox0
• J Hanselman, Bordered Heegaard–Floer homology and graph manifolds, PhD thesis, Columbia University (2014) \setbox0\makeatletter\@url http://search.proquest.com/docview/1528550664 {\unhbox0
• M Hedden, On knot Floer homology and cabling, II, Int. Math. Res. Not. 2009 (2009) 2248–2274
• J Hom, A note on cabling and $L$–space surgeries, Algebr. Geom. Topol. 11 (2011) 219–223
• T Kadokami, M Shimozawa, Dehn surgery along torus links, J. Knot Theory Ramifications 19 (2010) 489–502
• H,B Laufer, On rational singularities, Amer. J. Math. 94 (1972) 597–608
• P Lisca, A,I Stipsicz, Ozsváth–Szabó invariants and tight contact 3-manifolds, III, J. Symplectic Geom. 5 (2007) 357–384
• Y Liu, $L$–space surgeries on links (2013) To appear in Quantum Topol.
• A Némethi, On the Ozsváth–Szabó invariant of negative definite plumbed $3$–manifolds, Geom. Topol. 9 (2005) 991–1042
• W,D Neumann, A calculus for plumbing applied to the topology of complex surface singularities and degenerating complex curves, Trans. Amer. Math. Soc. 268 (1981) 299–344
• W,D Neumann, F Raymond, Seifert manifolds, plumbing, $\mu$–invariant and orientation reversing maps, from: “Algebraic and geometric topology”, (K,C Millett, editor), Lecture Notes in Math. 664, Springer, Berlin (1978) 163–196
• P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58–116
• P Ozsváth, Z Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. 159 (2004) 1027–1158
• P Ozsváth, Z Szabó, On knot Floer homology and lens space surgeries, Topology 44 (2005) 1281–1300
• P Ozsváth, Z Szabó, Holomorphic disks, link invariants and the multi-variable Alexander polynomial, Algebr. Geom. Topol. 8 (2008) 615–692
• M Spivakovsky, Sandwiched singularities and desingularization of surfaces by normalized Nash transformations, Ann. of Math. 131 (1990) 411–491