Parker, J. R. and Platis, I. D. (2008) 'Complex hyperbolic Fenchel-Nielsen coordinates.', Topology., 47 (2). pp. 101-135.
Let Σ be a closed, orientable surface of genus g. It is known that the 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.
|Keywords:||Complex hyperbolic geometry, Fenchel–Nielsen coordinates, Cross-ratio.|
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||http://dx.doi.org/10.1016/j.top.2007.08.001|
|Date accepted:||No date available|
|Date deposited:||17 November 2009|
|Date of first online publication:||March 2008|
|Date first made open access:||No date available|
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