Laurent Charles, Julien Marche
Published 2009-01-20Version 1
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.
Geometry of representation spaces in SU(2)
Deformations of metabelian representations of knot groups into $SL(3,\mathbb{C})$
On the SU(2,1) representation space of the Brieskorn homology spheres
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