nLab
unknot

Idea

The trivial knot.

Definition

An unknot is any knot isotopic to the flat circle embedded in the $(x,y)$-plane of $\mathbb{R}^3$.

References

See also

• Wikipedia, Unknot

Computation of the perturbative Wilson loop observable (universal Vassiliev invariant) of the unknot (“Wheels theorem”):

• Dror Bar-Natan, Thang T Q Le, Dylan Thurston, Two applications of elementary knot theory to Lie algebras and Vassiliev invariants, Geom. Topol. Volume 7, Number 1 (2003), 1-31 (euclid.gt/1513883092)

following

• Dror Bar-Natan, Stavros Garoufalidis, Lev Rozansky, Dylan Thurston, Wheels, wheeling, and the Kontsevich integral of the unknot (q-alg/9703025)