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A new state-sum formula for the evaluation of the Yang-Mills measure in theKauffman bracket skein algebra of a closed surface is derived. The formulaextends the Kauffman bracket to diagrams that lie in surfaces other than theplane. It also extends Turaev's shadow world invariant of links in a circlebundle over a surface away from roots of unity. The limiting behavior of theYang-Mills measure when the complex parameter approaches -1 is studied. Theformula is applied to compute integrals of simple closed curves over thecharacter variety of the surface against Goldman's symplectic measure.

Shadow world evaluation of the Yang–Mills measure