Positive lower-bound conjecture for conformal angle energy of non-trivial knots

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Let KK be a knot, and let ∣csl∣(K)|csl|(K) denote the absolute value of its conformal linking energy. Positive lower-bound conjecture. There is a positive constant CC such that, if KK is a non-trivial knot, then

∣csl∣(K)≥C.|csl|(K)\ge C.

Such a bound would separate non-trivial knots from the standard planar circle, for which the corresponding energy is zero. The source gives no resolution of this claim.

References

Primary source

R. Langevin and J. O'Hara, “Conformally invariant energies of knots”, arXiv:math/0409396 (2004).

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