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43
votes
Accepted
Kähler structure on cotangent bundle?
This is true! I assume $M$ compact.
Method 1. Real algebraic geometry. Cf. Fukaya, Seidel, and Smith - Exact Lagrangian submanifolds in simply-connected cotangent bundles. By a version of the Nash–To …
25
votes
Accepted
Can cotangent bundles see exotic smooth structures?
I wrote a little expository piece about this and related matters in the Newsletter of the European Mathematical Society:
http://www.ems-ph.org/journals/newsletter/pdf/2010-03-75.pdf
The classical to …