Algebraic & Geometric Topology

Heegaard Floer homology of certain mapping tori

Stanislav Jabuka and Thomas E Mark

Full-text: Open access


We calculate the Heegaard Floer homologies HF+(M,s) for mapping tori M associated to certain surface diffeomorphisms, where s is any spinc structure on M whose first Chern class is non-torsion. Let γ and δ be a pair of geometrically dual nonseparating curves on a genus g Riemann surface Σg, and let σ be a curve separating Σg into components of genus 1 and g1. Write tγ, tδ, and tσ for the right-handed Dehn twists about each of these curves. The examples we consider are the mapping tori of the diffeomorphisms tγmtδn for m,n and that of tσ±1.

Article information

Algebr. Geom. Topol., Volume 4, Number 2 (2004), 685-719.

Received: 6 July 2004
Accepted: 16 August 2004
First available in Project Euclid: 21 December 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R58: Floer homology
Secondary: 53D40: Floer homology and cohomology, symplectic aspects

Heegaard Floer homology mapping tori


Jabuka, Stanislav; Mark, Thomas E. Heegaard Floer homology of certain mapping tori. Algebr. Geom. Topol. 4 (2004), no. 2, 685--719. doi:10.2140/agt.2004.4.685.

Export citation


  • Eaman Eftekhary, Floer cohomology of certain pseudo-Anosov maps..
  • Ronald Fintushel and Ronald Stern, Using Floer's exact triangle to compute Donaldson invariants, The Floer memorial volume, Progr. Math. 133, Birkhäuser 1995, 435–444.
  • Michael Hutchings and Michael Sullivan, The periodic Floer homology of a Dehn twist, preprint at
  • I. G. Macdonald, Symmetric products of an algebraic curve, Topology 1 (1962), 319–343.
  • C. McMullen, The Alexander polynomial of a 3-manifold and the Thurston norm on cohomology, Ann. Scient. École Norm. Sup. 35 (2000), 153–171.
  • G. Meng and C. H. Taubes, SW = Milnor torsion, Math. Res. Lett. 3 (1996), 661–674.
  • Dean Neumann, 3-manifolds fibering over $S^1$, Proc. Amer. Math. Soc. 58 (1976), 353–356.
  • Peter Ozsváth and Zoltán Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003), 179–261.
  • Peter Ozsváth and Zoltán Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004), 58–116.
  • Peter Ozsváth and Zoltán Szabó, Holomorphic disks and three-manifold invariants: properties and applications..
  • Peter Ozsváth and Zoltán Szabó, Holomorphic disks and topological invariants for closed 3-manifolds..
  • Peter Ozsváth and Zoltán Szabó, Holomorphic triangles and invariants for smooth four-manifolds..
  • Peter Ozsváth and Zoltán Szabó, Holomorphic triangle invariants and the topology of symplectic four-manifolds, Duke Math. J. 121 (2004), 1–34.
  • Paul Seidel, The symplectic Floer homology of a Dehn twist, Math. Res. Lett. 3 (1996), 829–834.
  • William Thurston, A norm for the homology of 3-manifolds, Mem. Amer. Math. Soc. 59 (1986), No. 339, 99–130.
  • Jeffrey Tollefson, 3-manifolds fibering over $S^1$ with nonunique connected fiber, Proc. Amer. Math. Soc. 21 (1969), 79–80.