Variational methods in topology (published in Russian in 1982) based on a course which he taught to undergraduate and graduate students at Moscow State

as the " W'-measure" of the holonomy determined by the oriented knot k . In this way every pair (G, W) defines a numerical invariant on knots by its expectation value (Xw{k)} in the k-G theory, and Witten argues that these expectation values are related to the values of the Jones and Alexander polynomials at various roots of unity. For instance, when G = SU'(2) and W is the representation of "level k ," then according to Witten