On Einstein Metrics on 4-Manifolds with Finite Cyclic Fundamental Group

2008/04/30 by Ioana Şuvaina, Ioana Suvaina, Suvaina, Ioana
Mathematics · #14J29 #53C25 #57R57 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:14J29 #msc:53C25 #msc:57R57

paper · pdf · doi:10.48550/arxiv.0804.4823

new title, presentation improved

openalex publication_date 2008/04/30 · arxiv created 2016/10/10 · arxiv updated 2016/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The existence or non-existence of Einstein metrics on 4-manifolds with non-trivial fundamental group and the relation with the underlying differential structure are analyzed. For most points (n,m) in a large region of the integer lattice, the manifold n\mathbb C \mathbb P²#m \mathbb C \mathbb P² is shown to admit infinitely many inequivalent free actions of finite cyclic groups and there are no Einstein metrics which are invariant under any of these actions. The main tools are Seiberg-Witten theory, cyclic branched coverings of complex surfaces and symplectic surgeries.

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