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An ordinary knot in three dimensions suspended in four dimensions to create a knotted 2-sphere. Suspended knots are not smooth at the poles.

A knot which tightens around an object when strained but slackens when the strain is removed. Running knots are sometimes also known as slip knots or nooses.

A symmetry of a knot K is a homeomorphism of R^3 which maps K onto itself. More succinctly, a knot symmetry is a homeomorphism of the pair of spaces (R^3,K). Hoste et al. ...

A concise notation based on the concept of the tangle used by Conway (1967) to enumerate prime knots up to 11 crossings. An algebraic knot containing no negative signs in its ...

The exterior of a knot K is the complement of an open solid torus knotted like K. The removed open solid torus is called a tubular neighborhood (Adams 1994, p. 258).

The Kinoshita-Terasaka knot is the prime knot on eleven crossings with braid word ...

A knot K embedded in R^3=C_z×R_t, where the three-dimensional space R^3 is represented as a direct product of a complex line C with coordinate z and a real line R with ...

One of the "knots" t_(p+1), ..., t_(m-p-1) of a B-spline with control points P_0, ..., P_n and knot vector T={t_0,t_1,...,t_m}, where p=m-n-1.

A knot invariant in the form of a polynomial such as the Alexander polynomial, BLM/Ho Polynomial, bracket polynomial, Conway polynomial, HOMFLY polynomial, Jones polynomial, ...

An n-bridge knot is a knot with bridge number n. The set of 2-bridge knots is identical to the set of rational knots. If L is a 2-bridge knot, then the BLM/Ho polynomial Q ...