Minimal Discrepancy of Isolated Singularities and Reeb Orbits Continued

Mark Mclean

Recall from the previous lecture, if A is an isolated singularity satisfying additional conditions then there is an invariant md(A) called the minimal discrepancy. Also from the previous lecture, for a contact manifold C we introduced an invariant md(C) calculated using indices of Reeb orbits. In this lecture we will show (roughly) that md(A) is greater than or equal to md(L_A) where L_A is a contact manifold called the link of A. This is the easier half of the proof. After that we will begin to show (using pseudo holomorphic curve theory) that md(A) is less than or equal to md(L_A).

http://scgp.stonybrook.edu/video_portal/video.php?id=1557

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