In the mathematical theory of knots, a flype is a kind of manipulation of knot and

link diagram In the mathematical field of topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot ...

s used in the

Tait flyping conjecture The Tait conjectures are three conjectures made by 19th-century mathematician Peter Guthrie Tait in his study of knots.. The Tait conjectures involve concepts in knot theory such as alternating knots, chirality, and writhe. All of the Tait conje ...

. It consists of twisting a part of a knot, a

tangle Tangle may refer to: Science, Technology, Engineering & Mathematics *''The Tangle'' is the name of the ledger, a directed acyclic graph, used for the cryptocurrency IOTA *Tangle (mathematics), a topological object Natural sciences & medicine ...

T, by 180 degrees. Flype comes from a Scots word meaning ''to fold'' or ''to turn back'' ("as with a sock").. Tait used the term to mean, "a change of infinite complementary region"). Two reduced alternating diagrams of an alternating link can be transformed to each other using flypes. This is the

, proven in 1991 by

Morwen Thistlethwaite Morwen Bernard 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 Morwen Thistlethwait ...

and

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 his B.A. from the University of California, Los Angeles in 1975, and his Ph.D. from the Univ ...

References

Knot operations {{knottheory-stub

See also

References