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Quasipositive links and
Stein surfaces
Kyle Hayden |
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Geometry & Topology 25 (2021) 1441–1477
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Abstract |
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We study the generalization of quasipositive links from the –sphere to arbitrary closed, orientable –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 –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 – and –manifolds. |
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Keywords
Stein surfaces, complex curves, contact structures, open
books, braids, quasipositive links, transverse links
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Mathematical Subject Classification 2010
Primary: 57R17
Secondary: 32Q28, 57M25
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References |
Publication
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
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Authors |
| Kyle Hayden | |
| Columbia University New York, NY United States |
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