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Complex hyperbolic Fenchel-Nielsen coordinates

Parker, J.R.; Platis, I.D.

Complex hyperbolic Fenchel-Nielsen coordinates Thumbnail


I.D. Platis


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.


Parker, J., & Platis, I. (2008). Complex hyperbolic Fenchel-Nielsen coordinates. Topology (Oxford), 47(2), 101-135.

Journal Article Type Article
Publication Date Mar 1, 2008
Deposit Date Nov 6, 2009
Publicly Available Date Nov 17, 2009
Journal Topology
Print ISSN 0040-9383
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 47
Issue 2
Pages 101-135
Keywords Complex hyperbolic geometry, Fenchel–Nielsen coordinates, Cross-ratio.


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