Mathematical Research Letters
Volume 3 (1996)
Four-Manifolds without Einstein Metrics
Pages: 133 – 147
It is shown that there are infinitely many compact simply connected 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.