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

Némethi, András¹

¹ Department of Mathematics, Ohio State University, Columbus, Ohio 43210, USA

Geometry & topology, Tome 9 (2005) no. 2, pp. 991-1042.

Résumé

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.

Détail

DOI : 10.2140/gt.2005.9.991

Keywords: 3–manifolds, Ozsváth–Szabó Heegaard Floer homology, Seiberg–Witten invariants, Seifert manifolds, Lens spaces, Casson–Walker invariant, $\mathbb{Q}$–homology spheres, Reidemeister–Turaev torsion, normal surface singularities, rational singularities, elliptic singularities

Bibliographie

[1] M Artin, Some numerical criteria for contractability of curves on algebraic surfaces, Amer. J. Math. 84 (1962) 485

[2] M Artin, On isolated rational singularities of surfaces, Amer. J. Math. 88 (1966) 129

[3] R E Gompf, A I Stipsicz, 4–manifolds and Kirby calculus, Graduate Studies in Mathematics 20, American Mathematical Society (1999)

[4] H Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann. 146 (1962) 331

[5] H B Laufer, On rational singularities, Amer. J. Math. 94 (1972) 597

[6] H B Laufer, On minimally elliptic singularities, Amer. J. Math. 99 (1977) 1257

[7] C Lescop, Global surgery formula for the Casson–Walker invariant, Annals of Mathematics Studies 140, Princeton University Press (1996)

[8] I Luengo-Velasco, A Melle-Hernández, A Némethi, Links and analytic invariants of superisolated singularities, J. Algebraic Geom. 14 (2005) 543

[9] A Némethi, “Weakly” elliptic Gorenstein singularities of surfaces, Invent. Math. 137 (1999) 145

[10] A Némethi, Five lectures on normal surface singularities, from: "Low dimensional topology (Eger, 1996/Budapest, 1998)", Bolyai Soc. Math. Stud. 8, János Bolyai Math. Soc. (1999) 269

[11] A Némethi, Line bundles associated with normal surface singularities

[12] A Némethi, L I Nicolaescu, Seiberg–Witten invariants and surface singularities, Geom. Topol. 6 (2002) 269

[13] A Némethi, L I Nicolaescu, Seiberg–Witten invariants and surface singularities II: Singularities with good $\mathbb C^*$–action, J. London Math. Soc. $(2)$ 69 (2004) 593

[14] 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

[15] W D Neumann, Abelian covers of quasihomogeneous surface singularities, from: "Singularities, Part 2 (Arcata, Calif., 1981)", Proc. Sympos. Pure Math. 40, Amer. Math. Soc. (1983) 233

[16] L I Nicolaescu, Seiberg–Witten invariants of rational homology 3–spheres, Commun. Contemp. Math. 6 (2004) 833

[17] P Ozsváth, Z Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. $(2)$ 159 (2004) 1027

[18] P Ozsváth, Z Szabó, Holomorphic disks and three-manifold invariants: properties and applications, Ann. of Math. $(2)$ 159 (2004) 1159

[19] P Ozsváth, Z Szabó, Holomorphic triangle invariants and the topology of symplectic four-manifolds, Duke Math. J. 121 (2004) 1

[20] P Ozsváth, Z Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003) 179

[21] P Ozsváth, Z Szabó, On the Floer homology of plumbed three-manifolds, Geom. Topol. 7 (2003) 185

[22] H Pinkham, Normal surface singularities with $C^*$ action, Math. Ann. 227 (1977) 183

[23] J Stevens, Elliptic surface singularities and smoothings of curves, Math. Ann. 267 (1984) 239

[24] V Turaev, Torsion invariants of $\mathrm{Spin}^c$–structures on 3–manifolds, Math. Res. Lett. 4 (1997) 679