Conformally invariant energies of knots

Details Conformally invariant energies of knots Conformally invariant energies of knots

2004-09-21

arxiv.org/abs/math/0409396v2

Mathematics

Geometric Topology

66 pages, 25 figures, to appear in J. Institut Math. Jussieu

Scientific paper

Conformally invariant functionals on the space of knots are introduced via extrinsic conformal geometry of the knot and integral geometry on the space of spheres. Our functionals are expressed in terms of a complex-valued 2-form which can be considered as the cross-ratio of a pair of infinitesimal segments of the knot. We show that our functionals detect the unknot as the total curvature does, and that their values explode if a knot degenerates to a singular knot with double points.

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