Analysis of Contact Cauchy-Riemann Maps and Canonical Connection on Contact Manifolds, I

Rui Wang

In this talk, we explain the analysis of the following system of elliptic equation $$\overline\partial^\pi w = 0, \, d(w^*\lambda \circ j) = 0 $$ associated for each given contact triad $(Q,\lambda,J)$ on a contact manifold $(Q,\xi)$. We directly work with this equation on the contact manifold without involving the symplectization process. We explain the basic analytical ingredients towards the construction of moduli space of solutions, which we call contact instantons. We will indicate how one could define contact homology type invariants using such a moduli space, which is still in progress.

http://scgp.stonybrook.edu/video_portal/video.php?id=1570

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