Exotic smooth structures and symplectic forms on closed manifolds

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...

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Bibliographic Details
Published inGeometriae dedicata Vol. 132; no. 1; pp. 31 - 42
Main Authors Hajduk, Bogusław, Tralle, Aleksy
Format Journal Article
LanguageEnglish
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
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Summary: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 (known) positive answer to the original question of Benson and Gordon that there are no Kähler structures on exotic tori. We survey also other related results which give an evidence for the conjecture that there are no symplectic structures on exotic tori.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-007-9181-5