Complex hyperbolic Fenchel-Nielsen coordinates

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

doi:10.1016/j.top.2007.08.001

Complex hyperbolic Fenchel-Nielsen coordinates

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

Authors

Professor John Parker j.r.parker@durham.ac.uk
Professor

I.D. Platis

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.

Citation

Parker, J., & Platis, I. (2008). Complex hyperbolic Fenchel-Nielsen coordinates. Topology (Oxford), 47(2), 101-135. https://doi.org/10.1016/j.top.2007.08.001

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
DOI	https://doi.org/10.1016/j.top.2007.08.001
Keywords	Complex hyperbolic geometry, Fenchel–Nielsen coordinates, Cross-ratio.