Surgery, Yamabe invariant, and Seiberg-Witten theory

Details Surgery, Yamabe invariant, and Seiberg-Witten theory Surgery, Yamabe invariant, and Seiberg-Witten theory

2007-10-12

arxiv.org/abs/0710.2375v5

Mathematics

Differential Geometry

Scientific paper

By using the gluing formula of the Seiberg-Witten invariant, we compute the Yamabe invariant Y(X) of 4-manifolds X obtained by performing surgeries along points, circles or tori on compact Kaehler surfaces. For instance, if M is a compact Kaehler surface of nonnegative Kodaira dimension, and N is a smooth closed oriented 4-manifold with b_2^+(N)=0 and Y(N)>= 0, then we show that Y(M # N)=Y(M).

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