On the nonexistence of Einstein metric on 4-manifolds
Differential Geometry
2010-11-17 v3
Abstract
By using the gluing formulae of the Seiberg-Witten invariant, we show the nonexistence of Einstein metric on manifolds obtained from a 4-manifold with nontrivial Seiberg-Witten invariant by performing sufficiently many connected sums or appropriate surgeries along circles or homologically trivial 2-spheres with closed oriented 4-manifolds with negative definite intersection form.
Cite
@article{arxiv.0809.4891,
title = {On the nonexistence of Einstein metric on 4-manifolds},
author = {Chanyoung Sung},
journal= {arXiv preprint arXiv:0809.4891},
year = {2010}
}