Equivariant and Bott-type Seiberg-Witten Floer Homology: Part II

TL;DR

This paper develops new equivariant and Bott-type Seiberg-Witten Floer homology theories for 3-manifolds, demonstrating their invariance and establishing equivalences among different formulations.

Contribution

It introduces multiple versions of equivariant Floer homology for 3-manifolds and proves their equivalence and invariance under diffeomorphisms.

Findings

Constructed equivariant and Bott-type Floer homologies for 3-manifolds.

Proved the diffeomorphism invariance of these homologies.

Established equivalence among different versions of the theory.

Abstract

We construct equivariant and Bott-type Seiberg-Witten Floer homology and cohomology for 3-manifolds, in particular rational homology spheres, and prove their diffeomorphism invariance. We present several versions of the equivariant theory: the singular version, the de Rham version and the Cartan version, with the first playing the most important role. These versions are shown to be equivalent to each other. A few typos are removed.