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Cross-sections of unknotted ribbon disks and algebraic curves

Part of: Low-dimensional topology Complex manifolds

Published online by Cambridge University Press:  11 February 2019

Kyle Hayden
Kyle Hayden*
Affiliation:
Department of Mathematics, Columbia University, New York, NY 10027, USA email hayden@math.columbia.edu
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Abstract

We resolve parts (A) and (B) of Problem 1.100 from Kirby’s list [Problems in low-dimensional topology, in Geometric topology, AMS/IP Studies in Advanced Mathematics, vol. 2 (American Mathematical Society, Providence, RI, 1997), 35–473] by showing that many nontrivial links arise as cross-sections of unknotted holomorphic disks in the four-ball. The techniques can be used to produce unknotted ribbon surfaces with prescribed cross-sections, including unknotted Lagrangian disks with nontrivial cross-sections.

Keywords

ribbon surfacesalgebraic curvesLagrangian surfacesquasipositive links

MSC classification

Primary: 57M25: Knots and links in $S^3$
Secondary: 32Q55: Topological aspects of complex manifolds

Information

Type
Research Article
Information
Compositio Mathematica , Volume 155 , Issue 2 , February 2019 , pp. 413 - 423
Copyright
© The Author 2019 

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