Symplectic structures on cotangent bundles of open 4-manifolds

Geometry Topology Seminar
Monday, January 28, 2013 - 14:00
1 hour (actually 50 minutes)
Skiles 006
Columbia University
Given any smooth manifold, there is a canonical symplectic structure on its cotangent bundle. A long standing idea of Arnol'd suggests that the symplectic topology of the cotangent bundle should contain a great deal of information about the smooth topology of its base. As a contrast, I show that when X is an open 4-manifold, this symplectic structure on T^*X does not depend on the choice of smooth structure on X. I will also discuss the particular cases of smooth structures on R^4 and once-punctured compact 4-manifolds.