Given a compact surface , we consider the representation space
We show that the trace functions associated to multicurves on are linearly independent as functions on . The proof relies on the Fourier decomposition of the trace functions with respect to a torus action on associated to a pants decomposition of . Consequently the space of trace functions is isomorphic to the Kauffman skein algebra at of the thickened surface.
Cite this article
Laurent Charles, Julien Marché, Multicurves and regular functions on the representation variety of a surface in SU(2). Comment. Math. Helv. 87 (2012), no. 2, pp. 409–431DOI 10.4171/CMH/258