Einstein Metrics and Smooth Structures on Non-Simply Connected 4-Manifolds

Details Einstein Metrics and Smooth Structures on Non-Simply Connected 4-Manifolds Einstein Metrics and Smooth Structures on Non-Simply Connected 4-Manifolds

2008-04-30

arxiv.org/abs/0804.4823v1

Mathematics

Differential Geometry

Scientific paper

We analyze the existence or non-existence of Einstein metrics on 4-manifolds with non-trivial fundamental group and the relation with the differential structure considered. We conclude that for admissible pairs $(n,m)$ in a large region of the integer lattice, the manifold $n\mathbb C \mathbb P^2#m \bar{\mathbb C \mathbb P^2}$ admits infinitely many non-equivalent free actions of finite cyclic groups and there are no Einstein metrics which are group invariant. The main tools are Seiberg-Witten Theory, cyclic branched coverings of complex surfaces and symplectic surgeries.

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