On the nonexistence of Einstein metric on 4-manifolds

Details On the nonexistence of Einstein metric on 4-manifolds On the nonexistence of Einstein metric on 4-manifolds

2008-09-29

arxiv.org/abs/0809.4891v3

Mathematics

Differential Geometry

Scientific paper

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.

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