#### 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.

Notes on file formats
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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