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

### Laurent Charles

Université Pierre et Marie Curie VI, Paris, France### Julien Marché

École Polytechnique, Palaiseau, France

## Abstract

Given a compact surface $Σ$, we consider the representation space

$M(Σ)=Hom(π_{1}(Σ),SU(2))/SU(2).$

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.

## 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. 409–431

DOI 10.4171/CMH/258