List of knot theory topics

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Knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, R3. Two mathematical knots are equivalent if one can be transformed into the other via a deformation of R3 upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting the string or passing the string through itself.

History[edit]

Knots, links, braids[edit]

Notation used in knot theory:

General knot types[edit]

Links[edit]

General types of links:

Tangles[edit]

Braids[edit]

Operations[edit]

Invariants and properties[edit]

Mathematical problems[edit]

Lists[edit]