Surgery, Yamabe invariant, and Seiberg–Witten theory

By using the gluing formula of the Seiberg–Witten invariant, we compute the Yamabe invariant Y(X)Y(X) of 4-manifolds XX obtained by performing surgeries along points, circles or tori on compact Kähler surfaces. For instance, if MM is a compact Kähler surface of nonnegative Kodaira dimension, and NN is a smooth closed oriented 4-manifold with b2+(N)=0 and Y(N)≥0Y(N)≥0, then we show that Y(M#N)=Y(M).Y(M#N)=Y(M).