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Energy of knots and the infinitesimal cross ratio
Jun O'Hara
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Geometry & Topology Monographs 13
(2008) 421–445
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Abstract
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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
Möbius 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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Keywords
energy, knot, conformal geometry, cross
ratio
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Mathematical Subject Classification
Primary: 57M25
Secondary: 53A30
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Publication
Received: 30 May 2006
Revised: 9 May 2007
Accepted: 16 May 2007
Published: 19 March 2008
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