Kauffman brackets, character varieties, and triangulations of surfaces

@article{Bonahon2010KauffmanBC,
  title={Kauffman brackets, character varieties, and triangulations of surfaces},
  author={Francis Bonahon and Helen M. Wong},
  journal={arXiv: Geometric Topology},
  year={2010}
}
A Kauffman bracket on a surface is an invariant for framed links in the thickened surface, satisfying the Kauffman skein relation and multiplicative under superposition. This includes representations of the skein algebra of the surface. We show how an irreducible representation of the skein algebra usually specifies a point of the character variety of homomorphisms from the fundamental group of the surface to PSL_2(C), as well as certain weights associated to the punctures of the surface… 
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