Spin structures on the Seiberg-Witten moduli spaces

2004/04/15 by Hirofumi Sasahira, Sasahira, H.
Mathematics · #57R57 #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0404275

openalex publication_date 2004/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be an oriented closed 4-manifold and \cL be a spin^c structure on M. In this paper we prove that under a suitable condition the Seiberg-Witten moduli space has a canonical spin structure and its spin bordism class is an invariant for M. We show that the invariant for M=#_j=1^l M_j is not zero, where each M_j is a K3 surface or a product of two oriented closed surfaces with odd genus and l is 2 or 3. As a corollary, we obtain the adjunction inequality for M. Moreover we show that M # N does not admit Einstein metric for some N with b⁺(N)=0.

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