4-Manifolds without Einstein Metrics

Details 4-Manifolds without Einstein Metrics 4-Manifolds without Einstein Metrics

1995-11-27

arxiv.org/abs/dg-ga/9511015v2

Mathematics

Algebraic Geometry

9 pages, latex, with \Bbb font redefined for WWW use

Scientific paper

It is shown that there are infinitely many compact orientable smooth
4-manifolds which do not admit Einstein metrics, but nevertheless satisfy the
strict Hitchin-Thorpe inequality 2 chi > 3 |tau|. The examples in question
arise as non-minimal complex algebraic surfaces of general type, and the method
of proof stems from Seiberg-Witten theory.

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