In
knot theory
In topology, knot theory is the study of knot (mathematics), 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 be und ...
, 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 moves (I. twist move, II. poke move, and III. slide move).
See also
*
Knot sum
*
Murasugi sum
*
Mutation (knot theory)
In the mathematics, mathematical field of knot theory, a mutation is an knot operation, 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 pla ...
References
{{Knottheory-stub