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List of knot theory topics

From Wikipedia, the free encyclopedia

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 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]

Elementary treatment using polygonal curves[edit]

Invariants and properties[edit]

Mathematical problems[edit]

Theorems[edit]

Lists[edit]