Compatible contact structures of fibered Seifert links in homology 3-spheres

TL;DR

This paper characterizes when fibered Seifert multilinks in homology 3-spheres admit tight compatible contact structures, linking their properties to quasipositivity and cabling operations in 3-manifolds.

Contribution

It provides a necessary and sufficient condition for tightness of contact structures on fibered Seifert multilinks in homology 3-spheres, especially for positively twisted fibrations.

Findings

Criteria for tight contact structures in positively twisted Seifert fibrations

Determination of strongly quasipositivity of fibered Seifert links in S^3

Analysis of compatible contact structures under cabling operations

Abstract

We study compatible contact structures of fibered Seifert multilinks in homology 3-spheres and especially give a necessary and sufficient condition for the contact structure to be tight in the case where the Seifert fibration is positively twisted. As a corollary we determine the strongly quasipositivity of fibered Seifert links in the 3-sphere. We also study the compatible contact structures of cablings along links in any 3-manifolds.