Exotic smooth structures and symplectic forms on closed manifolds

• Published in: Geometriae dedicata Vol. 132; no. 1; pp. 31 - 42
• Main Authors: Hajduk, Bogusław, Tralle, Aleksy
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.03.2008
• Subjects: Algebraic Geometry; Convex and Discrete Geometry; Differential Geometry; Hyperbolic Geometry; Mathematics; Mathematics and Statistics; Original Paper; Projective Geometry; Topology; symplectic structure; Exotic smooth structure; Albanese map; 53C15; Kähler structure

In this paper we discuss relations between symplectic forms and smooth structures on closed manifolds. Our main motivation is the problem if there exist symplectic structures on exotic tori. This is a symplectic generalization of a problem posed by Benson and Gordon. We give a short proof of the (kn...