Geometry & Topology

On the Floer homology of plumbed three-manifolds

Peter Ozsváth and Zoltán Szabó

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We calculate the Heegaard Floer homologies for three-manifolds obtained by plumbings of spheres specified by certain graphs. Our class of graphs is sufficiently large to describe, for example, all Seifert fibered rational homology spheres. These calculations can be used to determine also these groups for other three-manifolds, including the product of a circle with a genus two surface.

Article information

Geom. Topol., Volume 7, Number 1 (2003), 185-224.

Received: 15 April 2002
Revised: 28 January 2003
Accepted: 9 March 2003
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R58: Floer homology
Secondary: 57M27: Invariants of knots and 3-manifolds 53D40: Floer homology and cohomology, symplectic aspects 57N12: Topology of $E^3$ and $S^3$ [See also 57M40]

plumbing manifolds Seifert fibered spaces Floer homology


Ozsváth, Peter; Szabó, Zoltán. On the Floer homology of plumbed three-manifolds. Geom. Topol. 7 (2003), no. 1, 185--224. doi:10.2140/gt.2003.7.185.

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  • S K Donaldson, Floer homology groups in Yang-Mills theory, volume 147 of Cambridge Tracts in Mathematics, Cambridge University Press (2002), with the assistance of M Furuta and D Kotschick
  • N D Elkies, A characterization of the ${Z}\sp n$ lattice, Math. Res. Lett. 2 (1995) 321–326
  • R Fintushel, R J Stern, Instanton homology of Seifert fibered homology three spheres, Proc. of the London Math. Soc. 61 (1990) 109–137
  • K A Frøyshov, The Seiberg-Witten equations and four-manifolds with boundary, Math. Res. Lett 3 (1996) 373–390
  • K A Frøyshov, An inequality for the h-invariant in instanton Floer theory (2001).
  • R E Gompf, A I Stipsicz, $4$-manifolds and Kirby calculus, volume 20 of Graduate Studies in Mathematics, American Mathematical Society (1999)
  • P A Kirk, E P Klassen, Representation spaces of Seifert fibered homology spheres, Topology 30 (1991) 77–95
  • P B Kronheimer, T S Mrowka, The genus of embedded surfaces in the projective plane, Math. Research Letters 1 (1994) 797–808
  • J W Morgan, The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifold, Mathematical Notes 44, Princeton University Press (1996)
  • T S Mrowka, P S Ozsváth, B Yu, Seiberg-Witten Monopoles on Seifert Fibered Spaces, Comm. in Analysis and Geometry 5 (1997) 685–793
  • P S Ozsváth, Z Szabó, Holomorphic triangles and invariants for smooth four-manifolds.
  • P S Ozsváth, Z Szabó, Holomorphic disks and three-manifold invariants: properties and applications (2001)., to appear in Annals of Math.
  • P S Ozsváth, Z Szabó, Holomorphic disks and topological invariants for closed three-manifolds (2001)., to appear in Annals of Math.
  • P S Ozsváth, Z Szabó, Holomorphic disk invariants for symplectic four-manifolds (2002).
  • P S Ozsváth, Z Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Advances in Mathematics 173 (2003) 179–261
  • P S Ozsváth, Z Szabó, On Heegaard Floer homology and Seifert fibered surgeries (2003).
  • E Witten, Monopoles and Four-Manifolds, Math. Research Letters 1 (1994) 769–796