Editing Unknot (section)

== Unknotting problem ==
{{main|Unknotting problem}}

Deciding if a particular knot is the unknot was a major driving force behind [[knot invariant]]s, since it was thought this approach would possibly give an efficient algorithm to [[unknotting problem|recognize the unknot]] from some presentation such as a [[knot diagram]]. Unknot recognition is known to be in both [[NP (complexity)|NP]] and [[co-NP]].

It is known that [[Heegaard Floer homology|knot Floer homology]] and [[Khovanov homology]] detect the unknot, but these are not known to be efficiently computable for this purpose.  It is not known whether the Jones polynomial or [[finite type invariant]]s can detect the unknot.