On geography of symplectic fillings of contact branched covers

Abstract

In this paper, we determine the Euler characteristics and signatures of the exact symplectic fillings of the contact double, 3-fold or 4-fold cyclic covers of the standard contact 3-sphere branched over certain transverse quasi-positive links. These links include all quasipositive knots with crossing numbers smaller than 11 and all quasi-positive links with crossing numbers smaller than 12 and nonzero nullity.