Exotic smooth structures and symplectic forms on closed manifolds

2006/12/31 by Bogusław Hajduk, Boguslaw Hajduk, Aleksy Tralle
Mathematics · #Algebraic geometry #Conjecture #Differential geometry #Generalization #Geometric and Algebraic Topology #Geometry #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Pure mathematics #Symplectic geometry #Symplectic manifold #Symplectic representation #Symplectomorphism #Torus #math.DG #math.SG #msc:53C15

paper · pdf · doi:10.1007/s10711-007-9181-5

published as Geom. Dedic. 132(2008), 31-42 · AMSLaTeX, 16 pages, a new version. A survey of the symplectic version of the problem is added

arxiv created 2007/04/04 · openalex publication_date 2007/08/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We give a short proof of the (known) result that there are no Kaehler structures on exotic tori. This yields a negative solution to a problem posed by Benson and Gordon. W discuss the symplectic version of the problem and analyze results which yield an evidence for the conjecture that there are no symplectic structures on exotic tori.

Citations

• Fundamental Groups of Compact Kähler Manifolds
• Solvable fundamental groups of algebraic varieties and Kähler manifolds
• Kähler Solvmanifolds