Shadow world evaluation of the Yang-Mills measure

Charles Frohman; Joanna Kania-Bartoszynska

doi:10.2140/agt.2004.4.311

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Shadow world evaluation of the Yang-Mills measure

Charles Frohman·Joanna Kania-Bartoszynska

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Abstract

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

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Charles Frohman, Joanna Kania-Bartoszynska. 2004-06-14. Shadow world evaluation of the Yang-Mills measure. https://doi.org/10.2140/agt.2004.4.311

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