Chanyoung Sung
Published 2008-09-29, updated 2010-11-16Version 3
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.
Einstein Metrics, Complex Surfaces, and Symplectic 4-Manifolds
Einstein metrics on connected sums of $S^2\times S^3$
Stability of Einstein metrics and effective hyperbolization
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