The self-linking number of a closed curve in Rⁿ

1999/06/02 by A. Montesinos-Amilibia, Montesinos-Amilibia, A., J. J. Nuno-Ballesteros +1
Mathematics · #53A04 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A04

paper · pdf · doi:10.48550/arxiv.math/9906015

13 pages; 2 figures; AMS-LaTeX

arxiv created 1999/06/02 · arxiv updated 2009/11/30

Abstract

We introduce the self-linking number of a smooth closed curve in Rⁿ with respect to a 3-dimensional vector bundle over the curve, provided that some regularity conditions are satisfied. When n=3, this construction gives the classical self-linking number of a closed embedded curve with non-vanishing curvature. We also look at some interesting particular cases, which correspond to the osculating or the orthogonal vector bundle of the curve.

Related

• Self-linked curves and normal bundle
• Self-linking number of a real algebraic link
• The Self-Linking Number in Planar Open Book Decompositions
• A Proof of the Invariant Based Formula for the Linking Number and its Asymptotic Behaviour
• Lines and circles joining components of a link