Möbius energy

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In mathematics, the Möbius energy of a knot is a particular knot energy, i.e. a functional on the space of knots. Its useful properties include blowing up as the knot's strands get close to one another (preventing self-intersection) and being invariant under Möbius transformations. The latter is particularly useful for showing the existence of an energy minimizer in each isotopy class of a prime knot. Conjecturally, there is no energy minimizer for composite knots.

[edit] References

• Jun Ohara, "Energy of knots", Topology and Its Applications, 1991
• M. Freedman, Z. He, ? Wang, "Möbius energy of knots and unknots", Annals of Mathematics