Quasipositive links and Stein surfaces
arXiv:1703.10150 · doi:10.2140/gt.2021.25.1441
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.
arXiv comment30 pages, 5 figures; comments welcome!
References in corpus (9)
- Géométrie de contact: de la dimension trois vers les dimensions supérieures
- Lectures on open book decompositions and contact structures
- Algebraic functions and closed braids
- Stabilization in the braid groups II: Transversal simplicity of knots
- Markov theorem for transversal links
- The Markov Theorem for transverse knots
- On the equivalence of Legendrian and transverse invariants in knot Floer homology
- Open Book Foliations
- Braiding Knots in Contact 3-Manifolds