Energy of knots and the infinitesimal cross ratio

Details Energy of knots and the infinitesimal cross ratio Energy of knots and the infinitesimal cross ratio

2007-08-22

arxiv.org/abs/0708.2948v2

Geom. Topol. Monogr. 13 (2008) 421-445

Mathematics

Geometric Topology

This is the version published by Geometry & Topology Monographs on 19 March 2008

Scientific paper

10.2140/gtm.2008.13.421

This is a survey article on two topics. The Energy E of knots can be obtained by generalizing an electrostatic energy of charged knots in order to produce optimal knots. It turns out to be invariant under Moebius transformations. We show that it can be expressed in terms of the infinitesimal cross ratio, which is a conformal invariant of a pair of 1-jets, and give two kinds of interpretations of the real part of the infinitesimal cross ratio.

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