\(U\)-action on perturbed Heegaard Floer homology (Q695357)

The purpose of this paper is to study the so-called Heegaard homology of some special classes of fibered 3-manifolds. As it is well-known, there are several versions of Floer homology (instanton Floer homology, Seiberg-Witten Floer homology, embedded contact homology) that can be viewed as siblings of Heegaard-Floer homology. These homologies have different origins, but it is largely believed that all of them should be isomorphic in some sense. The author computes the perturbed Heegaard-Floer homology for some special classes of fibered 3-manifolds, and establishes an adjunction inequality which indicates a potential connection between the \(U\)-action on the homology group and the Thurston norm of a 3-manifold.