Asian Journal of Mathematics

Volume 10 (2006)

Number 4

Mod $p$ vanishing theorem of Seiberg-Witten invariants for 4-manifolds with $\Bbb Z\sb p$-actions

Pages: 731 – 748



Nobuhiro Nakamura


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.

Published 1 January 2006