Title: The Yang-Mills measure in the Kauffman bracket skein module.

Abstract:

The quantum invariants of 3-manifolds are only defined at roots of unity. However, there is ample evidence that they exist as holomorphic functions on the unit disk, that diverge everywhere on the unit circle but at roots of unity. We take a step towards seeing that this holds in general, by showing that the Yang-Mills measure exists as a trace on the Kauffman bracket skein algebra of a closed surface F. When the deformation parameter t is a generic point on the unit circle, then the measure does not converge. At t=-1, the Yang-Mills measure is the integration against the symplectic measure on the SU(2) character variety of the fundamental group of the surface F.