Parker, J. R. and Platis, I. D. (2008) 'Complex hyperbolic Fenchel-Nielsen coordinates.', Topology., 47 (2). pp. 101-135.
Abstract
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 Download PDF (373Kb) |
| Status: | Peer-reviewed |
| 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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