Exotic smooth structures and symplectic forms on closed manifolds. (English) Zbl 1136.53059
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.
MSC:
| 53D35 | Global theory of symplectic and contact manifolds |
| 57R17 | Symplectic and contact topology in high or arbitrary dimension |
| 53D55 | Deformation quantization, star products |
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