# Quasipositive links and Stein surfaces

## TL;DR

This paper extends the concept of quasipositive links from the three-sphere to all closed, orientable three-manifolds, linking complex curves in Stein domains to quasipositive links via topological methods.

## Contribution

It proves that boundaries of complex curves in Stein domains are quasipositive links in general three-manifolds, broadening the understanding of link types bounding complex surfaces.

## Key findings

- Boundaries of complex curves in Stein domains are quasipositive links.
- Generalization of quasipositive links to arbitrary three-manifolds.
- Replacement of pseudoholomorphic techniques with topological foliation methods.

## Abstract

We study the generalization of quasipositive links from the three-sphere to arbitrary closed, orientable three-manifolds. Our main result shows that the boundary of any smooth, properly embedded complex curve in a Stein domain is a quasipositive link. This generalizes a result due to Boileau and Orevkov, and it provides the first half of a topological characterization of links in three-manifolds which bound complex curves in a Stein filling. Our arguments replace pseudoholomorphic curve techniques with a study of characteristic and open book foliations on surfaces in three- and four-manifolds.