Minimal Discrepancy of Isolated Singularities and Reeb Orbits

Mark Mclean

Let A be an affine variety inside a complex N dimensional vector space which either has an isolated singularity at the origin or is smooth at the origin. The intersection of A with a very small sphere turns out to be a contact manifold called the link of A. Any contact manifold contactomorphic to the link of A is said to be Milnor fillable by A. If the first Chern class of our link is 0 then we can assign an invariant of our singularity called the minimal discrepancy. We relate the minimal discrepancy with indices of certain Reeb orbits on our link. As a result we show that the standard contact 5 dimensional sphere has a unique Milnor filling up to normalization. This will be a 2-3 part talk with proofs discussed the following weeks.

http://scgp.stonybrook.edu/video_portal/video.php?id=1554

Simons- Program: Moduli Spaces of Pseudo-holomorphic curves and their applications to Symplectic Topology