On Einstein metrics on non-simply connected 4-manifolds

Jeudi 20 septembre 2007 14:00-15:00 - Suvaina Ioana - IHES

Résumé : The existence or non-existence of Einstein metrics on a topological
4-manifold is strongly related to the differential structure considered.
We show that there exist infinitely many topological 4-manifolds with finite cyclic fundamental group such that each manifold admits a smooth structure which supports an Einstein metric and infinitely many other structures on which no Einstein metric can exist. We complete this result with theorems about non-existence of Einstein metrics on manifolds with finitely presented fundamental group and discuss some nice corollaries.
The main tools are Seiberg-Witten theory, cyclic coverings of complex surfaces and symplectic surgeries.

Lieu : bât. 425 - 121-123

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