Mod $p$ vanishing theorem of Seiberg-Witten invariants for 4-manifolds with $\Bbb Z\sb p$-actions
نویسندگان
چکیده
منابع مشابه
MOD p VANISHING THEOREM OF SEIBERG-WITTEN INVARIANTS FOR 4-MANIFOLDS WITH Zp-ACTIONS
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 b1 ≥ 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.
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When a cyclic group G of prime order acts on a 4-manifold X , we prove a formula which relates the Seiberg-Witten invariants of X to those of X/G.
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It is shown that the quotients of Kähler surfaces under free anti-holomorphic involutions have vanishing Seiberg-Witten invariants. Various vanishing theorems have played important roles in gauge theory. The first among them, due to S. K. Donaldson [2], states that the Donaldson invariants vanish for any smooth closed oriented 4-manifold X which decomposes to a connected sum X1#X2 with b2 (X1) ...
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ژورنال
عنوان ژورنال: Asian Journal of Mathematics
سال: 2006
ISSN: 1093-6106,1945-0036
DOI: 10.4310/ajm.2006.v10.n4.a6