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Gauss diagram invariants for knots which are not closed braids

Published online by Cambridge University Press:  27 August 2003

THOMAS FIEDLER
THOMAS FIEDLER
Affiliation:
Laboratoire de Topologie et Géométrie, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse cedex, France. e-mail: [email protected]
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Abstract

A knot in a thickened surface $F^2 \times \mathbb{R}$ is called a global knot if its projection to $F^2$ is transversal to a vector field on this surface, which has at most critical points of index −1. Global knots generalize closed braids. We introduce new knot invariants of finite type which are trivial for all global knots. These invariants are a very effective tool for showing that a given knot in $F^2 \times \mathbb{R}$ is not isotopic to any global knot.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 135 , Issue 2 , September 2003 , pp. 335 - 348
Copyright
2003 Cambridge Philosophical Society

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