Dissolving four-manifolds and positive scalar curvature

2003/06/05 by B. Hanke, D. Kotschick, J. Wehrheim · 1 citation
Mathematics · #Advanced Operator Algebra Research #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #math.DG #math.GT #math.SG #msc:53C25 #msc:57R55 #msc:57R57

paper · pdf · doi:10.1007/s00209-003-0553-8

published as Math. Zeitschrift 245 (2003), 545--555. · 13 pages; to appear in Mathematische Zeitschrift

arxiv created 2003/06/05 · openalex publication_date 2003/11/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove that many simply connected symplectic four-manifolds dissolve after connected sum with only one copy of S²× S². For any finite group G that acts freely on the three-sphere we construct closed smooth four-manifolds with fundamental group G which do not admit metrics of positive scalar curvature, but whose universal covers do admit such metrics.

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