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Complex hyperbolic Fenchel-Nielsen coordinates.

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.

Item Type:Article
Keywords:Complex hyperbolic geometry, Fenchel–Nielsen coordinates, Cross-ratio.
Full text:(AM) Accepted Manuscript
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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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