Periodic Floer homology and Seiberg-Witten Floer cohomology

TL;DR

This paper establishes an isomorphism between a version of Seiberg-Witten Floer cohomology and periodic Floer homology for certain 3-manifolds, linking two important invariants in low-dimensional topology.

Contribution

It constructs a new isomorphism connecting Seiberg-Witten Floer cohomology with periodic Floer homology for mapping tori of surface automorphisms.

Findings

Proves an isomorphism between the two Floer theories.

Derives immediate topological consequences from the isomorphism.

Enhances understanding of the relationship between different Floer homologies.

Abstract

Various Seiberg-Witten Floer cohomologies are defined for a closed, oriented 3-manifold; and if it is the mapping torus of an area-preserving surface automorphism, it has an associated periodic Floer homology as defined by Michael Hutchings. We construct an isomorphism between a certain version of Seiberg-Witten Floer cohomology and the corresponding periodic Floer homology, and describe some immediate consequences.