Surgery, Yamabe invariant, and Seiberg-Witten theory
Differential Geometry
2010-11-09 v5
Abstract
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).
Cite
@article{arxiv.0710.2375,
title = {Surgery, Yamabe invariant, and Seiberg-Witten theory},
author = {Chanyoung Sung},
journal= {arXiv preprint arXiv:0710.2375},
year = {2010}
}