Mod r Vanishing Theorem of Seiberg-Witten Invariant for 4-Manifolds acted by Cyclic Group Z_r

2012/04/07 by Wenzhao Chen, Chen, Wenzhao
Mathematics · #57M60 #57N13 #57R13 #57R15 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:57M60 #msc:57N13 #msc:57R13 #msc:57R15

paper · pdf · doi:10.48550/arxiv.1204.1617

This paper has been withdraw due to a crucial error in equation 4.3

openalex publication_date 2012/04/07 · arxiv created 2012/04/11 · arxiv updated 2012/04/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, a vanishing theorem is stated and proved. If a 4-manifold M admits a smooth action by a cyclic group ℤ_r, then given an ℤ_r-equivariant Spin^c-structure C on M, the Seiberg-Witten invariant SW(C) is zero modulo r under some slight assumptions. Here r can be any positive integer. This theorem is a generalization of the mod p vanishing theorem when ℤ_p is prime order cyclic proved by F.Fang.

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