regular isotopy invariant

The bracket polynomial is one-variable knot polynomial related to the Jones polynomial. The bracket polynomial, however, is not a topological invariant, since it is changed by type I Reidemeister moves. However, the polynomial span of the bracket polynomial is a knot invariant, as is a normalized form involving the writhe. The bracket polynomial is occasionally given the grandiose name regular isotopy invariant. It is defined by 〈L〉(A, B, d) congruent sum_σ 〈L|σ〉 d^( left double bracketing bar σ right double bracketing bar ), where A and B are the "splitting variables, " σ runs through all "states" of L obtained by splitting the link, 〈L|σ〉 is the product of "splitting labels" corresponding to σ, and

Jones polynomial | Kauffman polynomial X | square bracket polynomial

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