Asian Journal of Mathematics
Volume 10 (2006)
Mod $p$ vanishing theorem of Seiberg-Witten invariants for 4-manifolds with $\Bbb Z\sb p$-actions
Pages: 731 – 748
We give an alternative proof of the mod $p$ vanishing theorem by F. Fang of Seiberg-Witten invariants under a cyclic group action of prime order, and generalize it to the case when $b\sb 1 \geq 1$. Although we also use the finite dimensional approximation of the monopole map as well as Fang, our method is rather geometric. Furthermore, non-trivial examples of mod $p$ vanishing are given.
4-manifolds; Seiberg-Witten invariants; group actions
2010 Mathematics Subject Classification
Primary 57R57, 57S17. Secondary 57M60.