Khovanov homology). The Jones polynomial is described as the Euler characteristic for this homology. Detection of the unknot It is an open question whether there is a nontrivial knot with Jones polynomial equal to that of the unknot. It is known that there are nontrivial links with Jones polynomial equal to that of the corresponding unlinks by the work of Morwen Thistlethwaite. It was shown by Kronheimer and Mrowka that there is no nontrivial knot with Khovanov homology equal to that of the unknot. See also HOMFLY polynomial Alexander polynomial Volume conjecture Chern–Simons theory Quantum group Notes References (explains the definition by bracket polynomial and its relation to Jones' formulation by braid representation) External links Links with trivial Jones polynomial by Morwen Thistlethwaite Knot theory Polynomials Knot invariants