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arXiv · 1703.10150

Quasipositive links and Stein surfaces

Kyle Hayden
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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.

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Kyle Hayden. 2017-03-29. Quasipositive links and Stein surfaces. https://doi.org/10.2140/gt.2021.25.1441

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