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Mathematische Zeitschrift

, Volume 286, Issue 1–2, pp 263–290 | Cite as

Analytic knots, satellites and the 4-ball genus

  • Burglind JörickeEmail author
Article

Abstract

Call a smooth knot (or smooth link) in the unit sphere in \(\mathbb {C}^2\) analytic (respectively, smoothly analytic) if it bounds a complex curve (respectively, a smooth complex curve) in the complex ball. Let K be a smoothly analytic knot. For a small tubular neighbourhood of K we give a sharp lower bound for the 4-ball genus of analytic links L contained in it.

Keywords

Knots Links 4-Ball genus Quasi-positive braids Satellite knots Braided links Branched coverings of open Riemann surfaces 

Mathematics Subject Classification

Primary 57M25 57M12 32B15 Secondary 14H30 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Humboldt-University BerlinBerlinGermany

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