Complex hyperbolic Fenchel-Nielsen coordinates

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

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
• Electronic ISSN: 1879-3215
• 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.
• Public URL: https://durham-repository.worktribe.com/output/1523485