Perturbed Floer Homology of some fibered three manifolds

TL;DR

This paper computes the perturbed Heegaard Floer homology for certain fibered three-manifolds, specifically those that are products of a surface and a circle, using a specially constructed Heegaard diagram.

Contribution

It introduces a specific Heegaard diagram for product three-manifolds and calculates their perturbed Floer homology, advancing computational techniques in 3-manifold topology.

Findings

Explicit computation of perturbed Floer homology for $\Sigma_g imes S^1$

Development of a specialized Heegaard diagram for these manifolds

Enhanced understanding of Floer homology in fibered 3-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 its perturbed Heegaard Floer homology.