Knot

Summary

A knot is a closed curve in three-dimensional space that does not cross itself, considered up to continuous deformation of the surrounding space. Formally it is an embedding of the circle in $\R^3$ or in the $3$-sphere. Knot theory asks when two knots are equivalent, and answers it with knot invariants such as the knot group and knot polynomials. Knots are also the basic examples in the study of 3-manifolds.