 The bracket polynomial plays an important role in unifying the Jones polynomial with other quantum invariants.In particular, Kauffman's interpretation of the Jones polynomial allows generalization to state sum invariants of 3-manifolds.Recently the bracket polynomial formed the basis for Mikhail Khovanov's construction of a homology for knots and links, creating
a stronger invariant than the Jones polynomial and such that the graded Euler characteristic of the Khovanov homology is equal to the original
Jones polynomial.