Perturbed Floer homology of some fibered three-manifolds

Abstract

In this paper, we write down a special Heegaard diagram for a given product three-manifold ${\Sigma }_g\times S^1$. We use the diagram to compute the perturbed ${HF}^{\wedge }$ for the $3$–torus and the perturbed ${HF}^{+}$ for nontorsion spin${}^c$–structures for ${\Sigma }_g\times S^1$ when $g\ge 2$.