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

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

2009-01-20

arxiv.org/abs/0901.3064v1

Mathematics

Geometric Topology

23 pages

Scientific paper

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.

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