  We consider the representation space of a compact surface, that is the space
of morphisms from the fundamental group to SU(2) up to conjugation. We show
that the trace functions associated to multicurves on the surface are linearly
independent as functions on the representation space. The proof relies on the
Fourier decomposition of the trace functions with respect to some torus action
provided by a pants decomposition. Consequently the space of trace functions is
isomorphic to the skein algebra at A=-1 of the thickened surface.
