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arXiv · 1204.1617

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

Wenzhao Chen
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Abstract

In this paper, a vanishing theorem is stated and proved. If a 4-manifold $M$ admits a smooth action by a cyclic group $\mathbb{Z}_r$, then given an $\mathbb{Z}_r$-equivariant $Spin^c$-structure $\mathcal{C}$ on $M$, the Seiberg-Witten invariant $SW\mathcal{(C)}$ 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 $\mathbb{Z}_p$ is prime order cyclic proved by F.Fang.

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Wenzhao Chen. 2012-04-07. Mod r Vanishing Theorem of Seiberg-Witten Invariant for 4-Manifolds acted by Cyclic Group Z_r. https://arxiv.org/abs/1204.1617

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