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RESEARCH PRODUCT

THE ZONE MODULUS OF A LINK

Rémi LangevinGrégoire-thomas Moniot

subject

CombinatoricsAlgebra and Number TheoryCorollaryHopf linkSplit linkMathematical analysisModulusMöbius energyDisjoint setsInvariant (mathematics)Upper and lower boundsMathematics

description

In this paper, we construct a conformally invariant functional for two-component links called the zone modulus of the link. Its main property is to give a sufficient condition for a link to be split. The zone modulus is a positive number, and its lower bound is 1. To construct a link with modulus arbitrarily close to 1, it is sufficient to consider two small disjoint spheres each one far from the other and then to construct a link by taking a circle enclosed in each sphere. Such a link is a split link. The situation is different when the link is non-split: we will prove that the modulus of a non-split link is greater than [Formula: see text]. This value of the modulus is realized by a special configuration of linked circles called the Clifford link. As a corollary, we show that if the thickness of a non-split two-component link embedded in S3 is equal to [Formula: see text], then the link is the standard geometric Hopf link.

yearjournalcountryeditionlanguage
2005-09-01Journal of Knot Theory and Its Ramifications
https://doi.org/10.1142/s0218216505004081