Unfolded Seiberg-Witten Floer spectra, I: Definition and invariance

TL;DR

This paper introduces new unfolded Seiberg-Witten Floer spectra for closed oriented 3-manifolds, generalizing previous spectra and providing computations for specific Seifert spaces, advancing the understanding of 3-manifold invariants.

Contribution

It defines new unfolded Seiberg-Witten Floer spectra for 3-manifolds, extending Manolescu's spectrum to broader classes and demonstrating their properties through examples.

Findings

Defined multiple versions of unfolded Seiberg-Witten Floer spectra.

Generalized Manolescu's Floer spectrum to rational homology 3-spheres.

Computed examples for Seifert spaces.

Abstract

Let $Y$ be a closed and oriented $3$-manifold. We define different versions of unfolded Seiberg-Witten Floer spectra for $Y$. These invariants generalize Manolescu's Seiberg-Witten Floer spectrum for rational homology $3$-spheres. We also compute some examples when $Y$ is a Seifert space.