Editing Jones polynomial (section)

==Detection of the unknot==
It is an [[open problem|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 [[unlink]]s by the work of [[Morwen Thistlethwaite]].<ref>{{Cite journal |last=Thistlethwaite |first=Morwen |date=2001-06-01 |title=Links with trivial jones polynomial |url=https://www.worldscientific.com/doi/abs/10.1142/S0218216501001050 |journal=Journal of Knot Theory and Its Ramifications |volume=10 |issue=4 |pages=641–643 |doi=10.1142/S0218216501001050 |issn=0218-2165}}</ref> It was shown by Kronheimer and Mrowka that there is no nontrivial knot with Khovanov homology equal to that of the unknot.<ref>{{Cite journal|title = Khovanov homology is an unknot-detector|journal = Publications Mathématiques de l'IHÉS|date = 2011-02-11|issn = 0073-8301|pages = 97–208|volume = 113|issue = 1|doi = 10.1007/s10240-010-0030-y|first1 = P. B.|last1 = Kronheimer|first2 = T. S.|last2 = Mrowka|arxiv = 1005.4346|s2cid = 119586228}}</ref>