On symplectic fillings of lens spaces

Source abstract

Let ξ ¯ st \overline \xi _\textrm {st} be the contact structure naturally induced on the lens space L ( p , q ) = S 3 / Z / p Z L(p,q)=S^3/\mathbb {Z}/p\mathbb {Z} by the standard contact structure ξ st \xi _\textrm {st} on the three–sphere S 3 S^3 . We obtain a complete classification of the symplectic fillings of ( L ( p , q ) , ξ ¯ st ) (L(p,q),\overline \xi _\textrm {st}) up to orientation–preserving diffeomorphisms. In view of our results, we formulate a conjecture on the diffeomorphism types of the smoothings of complex two–dimensional cyclic quotient singularities.