李友林教授,上海交通大学

In this talk, we apply Menke's JSJ decomposition for symplectic fillings to several families of contact 3-manifolds. Among other results, we complete the classification up to orientation-preserving diffeomorphism of strong symplectic fillings of lens spaces. For large families of contact structures on Seifert fibered spaces over S^2, we reduce the problem of classifying exact symplectic fillings to the same problem for universally tight or canonical contact structures. We show that exact symplectic fillings of contact manifolds obtained by surgery on certain Legendrian negative cables are the result of attaching a symplectic 2-handle to an exact symplectic filling of a lens space. This is joint work with Austin Christian.