Knot invariants

numerical invariant that describes the linking of two closed curves in three-dimensional space

knot invariant

function of a knot that takes the same value for equivalent knots

mathematical invariant of a knot or link

non-trivial knot which cannot be written as the knot sum of two non-trivial knots

fundamental group of a knot complement

thumb|right|A tricolored trefoil knot.In the mathematical field of knot theory, the tricolorability of a knot is the ability of a knot to be colored with three colors subject to certain rules. Tricolorability is an isotopy invariant, and hence can be used to distinguish between two different (non-isotopic) knots. In particular, since the unknot is not tricolorable, any tricolorable knot is necessarily nontrivial.

A knot with a diagram whose crossings alternate under, over, under, over, as one travels along each component

non-negative integer-valued knot invariant; least number of crossings in a knot diagram

knot invariant that is a polynomial

normalized hyperbolic volume of the complement of a hyperbolic knot