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

Abstract

Given a compact surface Σ, we consider the representation space M(Σ) = Hom(π1(Σ), SU(2))/ SU(2). We show that the trace functions associated to multicurves on Σ are linearly independent as functions on M(Σ). The proof relies on the Fourier decomposition of the trace functions with respect to a torus action on M(Σ) associated to a pants decomposition of Σ. Consequently the space of trace functions is isomorphic to the Kauffman skein algebra at A = - 1 of the thickened surface. © Swiss Mathematical Society.