Gluing formula for the stable cohomotopy version of Seiberg-Witten invariants along 3-manifolds with $b_1>0$

Abstract

We will define a version of Seiberg-Witten-Floer stable homotopy types for a closed, oriented 3-manifold $Y$ with $b_1(Y)>0$ and a spin-c structure $\mathfrak{c}$ on $Y$ with $c_1(\mathfrak{c})$ torsion under an assumption on $Y$. Using the Seiberg-Witten-Floer stable homotopy type, we will construct a gluing formula for the stable cohomotopy version of Seiberg-Witten invariants of a closed 4-manifold $X$ which has a decomposition $X=X_1{\cup }_Y{X}_2$ along $Y$.

References in corpus (1)

• Equivariant maps between sphere bundles over tori and KO-degree

Cited by in corpus (1)

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