Perturbed Floer Homology of some Fibered Three Manifolds II

TL;DR

This paper computes the perturbed Floer homology for specific fibered three-manifolds, including mapping tori of Dehn twists, advancing understanding of their topological invariants in certain spin^c-structures.

Contribution

It introduces a method to compute perturbed Floer homology for new classes of fibered three-manifolds, extending previous techniques.

Findings

Computed $HF^+$ for mapping tori of Dehn twists

Analyzed Floer homology in second highest spin^c-structures

Extended methods to special fibered three-manifolds

Abstract

Modifying the method of [21], we compute the perturbed $HF^+$ for some special classes of fibered three manifolds in the second highest spin$^c$-structures $S_{g-2}$. The special classes considered in this paper include the mapping tori of Dehn twists along a single non-separating curve and along a transverse pair of curves.