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.
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
Scots usually refers to something of, from, or related to Scotland, including:
* Scots language, a language of the West Germanic language family native to Scotland
* Scots people, a nation and ethnic group native to Scotland
* Scoti, a Latin na ...
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
Alternating may refer to:
Mathematics
* Alternating algebra, an algebra in which odd-grade elements square to zero
* Alternating form, a function formula in algebra
* Alternating group, the group of even permutations of a finite set
* Alternati ...
can be transformed to each other using flypes. This is the
Tait flyping conjecture, 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 Unive ...
.
See also
*
Reidemeister move
Kurt Werner Friedrich Reidemeister (13 October 1893 – 8 July 1971) was a mathematician born in Braunschweig (Brunswick), Germany.
Life
He was a brother of Marie Neurath.
Beginning in 1912, he studied in Freiburg, Munich, Marburg, and Götting ...
s are another commonly studied kind of manipulation to knot diagrams.
References
Knot operations
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