1998/01/16 by D. Kotschick
Mathematics · #Combinatorics #Curvature #Diffeomorphism #Einstein #Einstein manifold #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Geometry and complex manifolds #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Metric (unit) #Pure mathematics #Scalar curvature #Sectional curvature #Topology (electrical circuits) #math.DG #math.GT #msc:14J29 #msc:53C25 #msc:57R55 #msc:57R57
paper · pdf · doi:10.2140/gt.1998.2.1
published as Geom. Topol. 2 (1998) 1-10 · 10 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol2/paper1.abs.html
arxiv created 1998/01/16 · openalex publication_date 1998/01/16 · arxiv updated 2014/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove that there are infinitely many pairs of homeomorphic non-diffeomorphic smooth 4-manifolds, such that in each pair one manifold admits an Einstein metric and the other does not. We also show that there are closed 4-manifolds with two smooth structures which admit Einstein metrics with opposite signs of the scalar curvature.