Invariants
The Alexander polynomial, Conway polynomial and Jones polynomial of the unknot are trivial:
No other knot with 10 or fewer 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 knot group of the unknot is an infinite cyclic group, and the knot complement is homeomorphic to a solid torus.
Read more about this topic: Unknot