Complex Hyperbolic Fenchel-nielsen Coordinates
نویسندگان
چکیده
Let Σ be a closed, orientable surface of genus g. It is known that the SU(2, 1) representation variety of π1(Σ) has 2g− 3 components of (real) dimension 16g− 16 and two components of dimension 8g−6. Of special interest are the totally loxodromic, faithful (that is quasi-Fuchsian) representations. In this paper we give global real analytic coordinates on a subset of the representation variety that contains the quasi-Fuchsian representations. These coordinates are a natural generalisation of Fenchel-Nielsen coordinates on the Teichmüller space of Σ and complex Fenchel-Nielsen coordinates on the (classical) quasi-Fuchsian space of Σ.
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