quasibraiding

Quasibraiding is a concept in the field of topology and knot theory, which studies the properties of knots and links in three-dimensional space. It is a generalization of the braiding operation, which involves interchanging two strands of a knot or link in a specific manner. In a braiding operation, the strands are interchanged in a way that preserves their orientation, while in a quasibraiding operation, the strands are interchanged in a way that reverses their orientation.

Quasibraiding was first introduced by Louis Kauffman in 1990 as a way to study the Jones polynomial, a knot invariant that encodes information about the topology of a knot. The Jones polynomial is a Laurent polynomial in a variable t, and it is defined by a skein relation, which relates the polynomial of a knot to the polynomials of its "skein" (a family of knots obtained by performing a local operation on the knot). The skein relation for the Jones polynomial involves a quasibraiding operation, which allows one to express the polynomial of a knot in terms of the polynomials of its skein.

Quasibraiding has since been studied in its own right, and it has been used to study other knot invariants, such as the HOMFLY polynomial and the Kauffman polynomial. It has also been used to study the relationship between knot theory and statistical mechanics, as the Jones polynomial can be interpreted as a partition function for a certain statistical mechanical model.