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We consider the representation space of a compact surface, that is the spaceof morphisms from the fundamental group to SU(2) up to conjugation. We showthat the trace functions associated to multicurves on the surface are linearlyindependent as functions on the representation space. The proof relies on theFourier decomposition of the trace functions with respect to some torus actionprovided by a pants decomposition. Consequently the space of trace functions isisomorphic to the skein algebra at A=-1 of the thickened surface.

Multicurves and regular functions on the representation variety of a surface in SU(2)