## Geometry & Topology

### On the Ozsvath-Szabo invariant of negative definite plumbed 3-manifolds

András Némethi

#### Abstract

The main goal of the present article is the computation of the Heegaard Floer homology introduced by Ozsváth and Szabó for a family of plumbed rational homology 3–spheres. The main motivation is the study of the Seiberg–Witten type invariants of links of normal surface singularities.

#### Article information

Source
Geom. Topol., Volume 9, Number 2 (2005), 991-1042.

Dates
Accepted: 13 April 2005
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513799610

Digital Object Identifier
doi:10.2140/gt.2005.9.991

Mathematical Reviews number (MathSciNet)
MR2140997

Zentralblatt MATH identifier
1138.57301

#### Citation

Némethi, András. On the Ozsvath-Szabo invariant of negative definite plumbed 3-manifolds. Geom. Topol. 9 (2005), no. 2, 991--1042. doi:10.2140/gt.2005.9.991. https://projecteuclid.org/euclid.gt/1513799610

#### References

• M Artin, Some numerical criteria for contractibility 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
• R E Gompf, I A Stipsicz, An Introduction to $4$–Manifolds and Kirby Calculus, Graduate Studies in Mathematics 20, Amer. Math. Soc. (1999)
• H Grauert, Über Modifikationen und exceptionelle analytische Mengen, Math. Ann. 146 (1962) 331–368
• H B Laufer, On rational singularities, Amer. J. Math. 94 (1972) 597–608
• H B Laufer, On minimally elliptic singularities, Amer. J. Math. 99 (1977) 1257–1295
• C Lescop, Global Surgery Formula for the Casson–Walker Invariant, Annals of Mathematics Studies 140, Princeton University Press (1996)
• I Luengo, A Melle-Hernández, A Némethi, Links and analytic invariants of superisolated singularities, J. Algebraic Geom. 2 (1993) 1–23
• A Némethi, “Weakly” Elliptic Gorenstein Singularities of Surfaces, Invent. Math. 137 (1999) 145–167
• A Némethi, Five lectures on normal surface singularities, from: “Low dimensional topology (Eger 1996/Budapest 1998)”, Bolyai Soc. Math. Stud. 8 (1999) 269–351
• A Némethi, Line bundles associated with normal surface singularities.
• A Némethi, L I Nicolaescu, Seiberg–Witten invariants and surface singularities, \gtref620029269328
• A Némethi, L I Nicolaescu, Seiberg–Witten invariants and surface singularities II (singularities with good $\C^*$–action), J. London Math. Soc. 69 (2004) 593–607
• 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 Neumann, Abelian covers of quasihomogeneous surface singularities, from: “Singularities Part 2 (Arcata Calif. 1981)”, Proc. Sympos. Pure Math. 40 (1983) 233–244
• L I Nicolaescu, Seiberg–Witten invariants of rational homology 3–spheres, Commun. Contemp. Math. 6 (2004) 833–866
• P S Ozsváth, Z Szabó, Holomorphic discs and topological invariants for closed three-spheres, Ann. of Math. (2) 159 (2004) 1027–1158
• P S Ozsváth, Z Szabó, Holomorphic discs and three-manifold invariants: properties and applications, Ann. of Math. (2) 159 (2004) 1159–1245
• P S Ozsváth, Z Szabó, Holomorphic triangle invariants and the topology of symplectic four-manifolds, Duke Math. J. 121 (2004) 1–34
• P S Ozsváth, Z Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundaries, Adv. Math. 173 (2003) 179–261
• P S Ozsváth, Z Szabó, On the Floer homology of plumbed three-manifolds, \gtref720035185224
• H Pinkham, Normal surface singularities with ${\C}^*$ action, Math. Ann. 117 (1977) 183–193
• J Stevens, Elliptic surface singularities and smoothing of curves, Math. Ann. 267 (1984) 239–249
• V G Turaev, Torsion invariants of $\Spin^c$–structures on $3$–manifolds, Math. Res. Lett. 4 (1997) 679–695