Gluing formula for the stable cohomotopy version of Seiberg-Witten invariants along 3-manifolds with b₁ > 0

2014/08/12 by Sasahira, H. · 1 citation
#57R57 #57R58 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1408.2623

Abstract

We will define a version of Seiberg-Witten-Floer stable homotopy types for a closed, oriented 3-manifold Y with b₁(Y) > 0 and a spin-c structure \mathfrakc on Y with c₁(\mathfrakc) 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 = X₁ ∪_Y X₂ along Y.

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