Trace Coordinates on Fricke spaces of some simple hyperbolic surfaces

  title={Trace Coordinates on Fricke spaces of some simple hyperbolic surfaces},
  author={William M. Goldman},
  journal={arXiv: Geometric Topology},
  • W. Goldman
  • Published 11 January 2009
  • Mathematics
  • arXiv: Geometric Topology
The conjugacy class of a generic unimodular 2 by 2 complex matrix is determined by its trace, which may be an arbitrary complex number. In the nineteenth century, it was known that a generic pair (X,Y) of such pairs is determined up to conjugacy by the triple of traces (tr(X),tr(Y),tr(XY), which may be an arbitary element of C^3. This paper gives an elementary and detailed proof of this fact, which was published by Vogt in 1889. The folk theorem describing the extension of a representation to a… 

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