unknot

The unknot is the knot with a projection containing no crossings, or equivalently the knot with three vertices. The unknot forms an identity when working with the connected sum of knots; that is, if $U$ is the unknot, then $K=K\#U$ for any knot $K$.

Title unknot Unknot 2013-03-22 13:17:24 2013-03-22 13:17:24 basseykay (877) basseykay (877) 6 basseykay (877) Definition msc 57M25 trivial knot KnotTheory