#### Volume 25, issue 3 (2021)

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### Kyle Hayden

Geometry & Topology 25 (2021) 1441–1477
##### Abstract

We study the generalization of quasipositive links from the $3$–sphere to arbitrary closed, orientable $3$–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 $3$–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 $3$– and $4$–manifolds.

##### Keywords
Stein surfaces, complex curves, contact structures, open books, braids, quasipositive links, transverse links
##### Mathematical Subject Classification 2010
Primary: 57R17
Secondary: 32Q28, 57M25