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KNOT SINGULARITIES OF HARMONIC MORPHISMS

Published online by Cambridge University Press:  20 January 2009

Paul Baird
Paul Baird
Affiliation:
Département de Mathématiques, Université de Bretagne Occidentale, 6 Avenue Le Gorgeu, BP 452, 29275 Brest Cedex, FR (Paul.Baird@univ-brest.fr)
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Abstract

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A harmonic morphism defined on $\mathbb{R}^3$ with values in a Riemann surface is characterized in terms of a complex analytic curve in the complex surface of straight lines. We show how, to a certain family of complex curves, the singular set of the corresponding harmonic morphism has an isolated component consisting of a continuously embedded knot.

AMS 2000 Mathematics subject classification: Primary 57M25. Secondary 57M12; 58E20

Keywords

knotknot singularityharmonic morphismalgebraic curve
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 1 , February 2001 , pp. 71 - 85
Copyright
Copyright © Edinburgh Mathematical Society 2001