Algebraic and Geometric Topology 4 (2004), paper no. 31, pages 685-719.

Heegaard Floer homology of certain mapping tori

Stanislav Jabuka, Thomas Mark

Abstract. We calculate the Heegaard Floer homologies$HF^+(M,s) for mapping tori M associated to certain surface diffeomorphisms, where s is any Spin^c structure on M whose first Chern class is non-torsion. Let gamma and delta be a pair of geometrically dual nonseparating curves on a genus g Riemann surface Sigma_g, and let sigma be a curve separating Sigma_g into components of genus 1 and g-1. Write t-gamma, t_delta, and t_sigma for the right-handed Dehn twists about each of these curves. The examples we consider are the mapping tori of the diffeomorphisms t_gamma^m circ t_delta^n for m,n in Z and that of t_sigma^{+-1}.

Keywords. Heegaard Floer homology, mapping tori

AMS subject classification. Primary: 57R58. Secondary: 53D40.

DOI: 10.2140/agt.2004.4.685

E-print: arXiv:math.GT/0405314

Submitted: 6 July 2004. Accepted: 16 August 2004. Published: 9 September 2004.

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Stanislav Jabuka, Thomas Mark
Department of Mathematics, Columbia University
2990 Broadway, New York, NY 10027, USA
and
Department of Mathematics, Southeastern Louisiana University
1205 North Oak Street, Hammond, LA 70402, USA

Email: jabuka@math.columbia.edu, Thomas.Mark@selu.edu

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