In
knot theory, a knot move or operation is a change or changes which preserve
crossing number.
Operations are used to investigate whether knots are equivalent,
prime
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
or
reduced.
Knot moves or operations include the
flype,
Habiro move, Markov moves (I. conjugation and II. stabilization),
pass move,
Perko move, and
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 Göttinge ...
s (I. twist move, II. poke move, and III. slide move).
See also
*
Knot sum
In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds. Its effect is to join two given manifolds together near a chosen point on each. This construction plays a key role in the classifi ...
*
Mutation (knot theory)
In the mathematical field of knot theory, a mutation is an operation on a knot that can produce different knots. Suppose ''K'' is a knot given in the form of a knot diagram. Consider a disc ''D'' in the projection plane of the diagram whose bo ...
References
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