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Quasipositive links and Stein surfaces

Kyle Hayden

Geometry & Topology 25 (2021) 1441–1477

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.

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Stein surfaces, complex curves, contact structures, open books, braids, quasipositive links, transverse links
Mathematical Subject Classification 2010
Primary: 57R17
Secondary: 32Q28, 57M25
Received: 5 June 2017
Revised: 14 April 2020
Accepted: 16 May 2020
Published: 20 May 2021
Proposed: András I Stipsicz
Seconded: Cameron Gordon, Peter Ozsváth
Kyle Hayden
Columbia University
New York, NY
United States