Editing Unknot (section)

== Invariants ==
The [[Alexander-Conway polynomial|Alexander–Conway polynomial]] and [[Jones polynomial]] of the unknot are trivial:
: <math>\Delta(t) = 1,\quad \nabla(z) = 1,\quad V(q) = 1.</math>

No other knot with 10 or fewer [[crossing number (knot theory)|crossings]] has trivial Alexander polynomial, but the [[Kinoshita–Terasaka knot]] and [[Conway knot]] (both of which have 11 crossings) have the same Alexander and Conway polynomials as the unknot. It is an open problem whether any non-trivial knot has the same Jones polynomial as the unknot.

The unknot is the only knot whose [[knot group]] is an infinite [[cyclic group]], and its [[knot complement]] is [[homeomorphism|homeomorphic]] to a [[solid torus]].