In the mathematical theory of knots

Knot theory

In topology, 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...

, a flype is a kind of manipulation of knot and link diagrams
used in the Tait flyping conjecture

Tait conjectures

The Tait conjectures are conjectures made by Peter Guthrie Tait in his study of knots. The Tait conjectures involve concepts in knot theory such as alternating knots, chirality, and writhe...

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It consists of twisting a part of a knot, a tangle: T by 180 degrees. Flype comes from an old Scottish word meaning to fold or to turn back. Two reduced alternating diagrams of an alternating link can be transformed to each other using flypes. This is the Tait flyping conjecture, proven in 1991 by Morwen Thistlethwaite

Morwen Thistlethwaite

Morwen B. Thistlethwaite is a knot theorist and professor of mathematics for the University of Tennessee in Knoxville. He has made important contributions to both knot theory, and Rubik's cube group theory.-Biography:...

 and William Menasco

William Menasco

William W. Menasco is a topologist and a professor at the University at Buffalo. He is best known for his work in knot theory.-Biography:Menasco received is B.A. from the University of California, Los Angeles in 1975, and his Ph.D. from the University of California, Berkeley in 1981, where his...

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See also

• Reidemeister moves are another commonly studied kind of manipulation to knot diagrams.