The Yang-Mills measure in the Kauffman bracket skein module

Abstract

For each closed, orientable surface g, we construct a local, diffeomorphism invariant trace on the Kauffman bracket skein module Kt(g I). The trace is defined when |t| is neither 0 nor 1, and at certain roots of unity. At t = -1, the trace is integration against the symplectic measure on the SU(2) character variety of the fundamental group of g.