Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T23:45:54.906Z Has data issue: false hasContentIssue false
  • English
  • Français

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: fiedler@picard.ups.else.fr
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)