On geography of symplectic fillings of contact branched covers

TL;DR

This paper calculates topological invariants like Euler characteristics and signatures for symplectic fillings of certain branched covers of the contact 3-sphere, focusing on specific classes of quasi-positive links.

Contribution

It provides explicit topological data for symplectic fillings of cyclic covers over a broad class of quasi-positive links, expanding understanding of their structure.

Findings

Euler characteristics and signatures are determined for these fillings.

Results cover all quasi-positive knots with crossing number <11.

Results include all quasi-positive links with crossing number <12 and nonzero nullity.

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 quasi-positive knots with crossing numbers smaller than 11 and all quasi-positive links with crossing numbers smaller than 12 and nonzero nullity.