UCLA

We define splitting surfaces in contact manifolds, and develop a technique for decomposing the strong or exact symplectic fillings of a contact manifold which admits such a surface, using Eliashberg’s strategy of filling by holomorphic discs. We then apply this technique to the symplectic filling classification problem for several families of contact manifolds. In particular, we complete the classification of exact fillings for lens spaces, virtually overtwisted torus bundles, and virtually overtwisted circle bundles over Riemann surfaces. We also produce classification results for contact manifolds obtained by surgery on Legendrian negative cables, and for large families of contact structures on Seifert fibered spaces.