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 , 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. 409–431

DOI 10.4171/CMH/258