Slice knots and links

simplest non-trivial closed knot with three crossings

right|150px|thumb|Two simple diagrams of the unknot In the mathematical theory of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Intuitively, the unknot is a closed loop of rope without a knot tied into it, unknotted. To a knot theorist, an unknot is any embedded topological circle in the 3-sphere that is ambient isotopic (that is, deformable) to a geometrically round circle, the standard unknot.

prime knot with 11 crossings named for John Horton Conway

knot with slice genus 0

mathematical knot with crossing number 6

connected sum of two trefoil knots with opposite chirality