Quasipositive links and Stein surfaces

Hayden, Kyle

doi:10.2140/gt.2021.25.1441

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Quasipositive links and Stein surfaces

Kyle Hayden

Geometry & Topology 25 (2021) 1441–1477

DOI: 10.2140/gt.2021.25.1441

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

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

Authors

Kyle Hayden
Columbia University New York, NY United States

Volume 25, issue 3 (2021)