Seiberg-Witten Floer homology and symplectic forms on S^1 X M^3

TL;DR

This paper investigates the relationship between Seiberg-Witten Floer homology and symplectic structures on S^1 x M, establishing conditions under which M fibers over the circle based on symplectic form properties.

Contribution

It proves that if S^1 x M admits a symplectic form with non-torsion canonical class and M has first Betti number 1, then M fibers over the circle.

Findings

M fibers over the circle under specified conditions

S^1 x M admits a symplectic form with non-torsion canonical class

Seiberg-Witten Floer homology relates to fibered structures

Abstract

Let M be a closed, connected, orientable 3-manifold. The purpose of this paper is to study the Seiberg-Witten Floer homology of M given that S^1 X M admits a symplectic form. In particular, we prove that M fibers over the circle if M has first Betti number 1 and S^1 X M admits a symplectic form with non-torsion canonical class.