Also, in knot theory, algebraic objects, such as polynomials or numbers, are assigned to knots and called knot invariants. Some of them are defined by recursive formula by changing the crossing points. Such change of crossing points are similar to the changes made by enzymes mentioned above. Hence, theories of knot invariants may be useful in the search for more general theories and 3D methods of computations. The knot invariants called Jones polynomial discovered in 1980s dramatically changed the area knot theory, and the new relation between knots and algebra was further applied to triangulated manifolds, and formed a new area called quantum topology.
Manifolds are geometric objects, such as surfaces and solids.
These methods produce manifold invariants from given triangulations. In these theories, generalizations of Penrose's spin network are used, in which graphs and all possible cycles are considered. Thus it is expected that 3D DNA computations be applied to such algebraic context in representation theories and q -deformations of algebraic structures.