Complex hyperbolic Kleinian groups with limit set a wild knot.
type: Item
instance of: scholarly article
title: Complex hyperbolic Kleinian groups with limit set a wild knot.
zbMATH Open document ID: 1051.30038
author: Francisco Dutenhefner
author: Nikolay Gusevskii
published in: Topology
publication date: 2004-05-27T00:00:00Z
review text: The authors construct explicitly a discrete representation \(\rho_{0}\) into \(PU(2,1)\) of a co-finite area Fuchsian group \(F< \text{PSL}(2,{\mathbb R})\) (which is a free group of finite rank) so that \(\rho_{0}(F)\) has a wild knot as limit set. In particular, they are able to see that the Teichmüller space of \(F\) (the \(PU(2,1)\) equivalence classes of all discrete representations of \(F\) into \(PU(2,1)\)) is not connected and that Toledo's invariant cannot identify different connected components of it.
reviewed by: Rubén A. Hidalgo
Mathematics Subject Classification ID: 30F40
Mathematics Subject Classification ID: 20H10
Mathematics Subject Classification ID: 30F60
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 57M07
Mathematics Subject Classification ID: 57S30
zbMATH DE Number: 2069741
zbMATH Keywords: complex hyperbolic Kleinian groups
zbMATH Keywords: Teichmüller space
zbMATH Keywords: Toledo's invariant
MaRDI profile type: Publication
full work available at URL: j.top.2003.10.004
OpenAlex ID: W2085152880
DOI: 10.1016/J.TOP.2003.10.004
description: scientific article; zbMATH DE number 2069741