Compactification via the real spectrum of spaces of classes of representations in \(SO(n,1)\)
type: Item
instance of: scholarly article
title: Compactification via the real spectrum of spaces of classes of representations in \(SO(n,1)\)
zbMATH Open document ID: 0803.32015
author: Taoufik Bouzoubaa
publication date: 1995-01-02T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75065
review text: Let \(\Gamma\) be a finitely generated non-elementary group. We denote the set of all \(n\)-dimensional hyperbolic structures on \(\Gamma\) by \(D^ n (\Gamma)\). \(D^ n (\Gamma)\) can be realized as a closed subset of a real algebraic set, which has a natural real compactification, denoted by \(\overline {D^ n (\Gamma)}^{sp}\). Our goal here is to describe the boundary points of \(\overline {D^ n (\Gamma)}^{sp}\). We obtain from the boundary points of this compactification certain representations of \(\Gamma\) into \(SO^ +_ F(n,1)\), where \(F(\supset \mathbb{R})\) is a non- Archimedean real closed field. By constructing a tree, as quotient space of hyperbolic \(n\)-space over \(F\), we find the same description of boundary points as Morgan's is: as representations into the isometry groups of \(\mathbb{R}\)-trees.
Mathematics Subject Classification ID: 32J05
Mathematics Subject Classification ID: 14P10
Mathematics Subject Classification ID: 57Q15
Mathematics Subject Classification ID: 20G99
zbMATH DE Number: 672144
zbMATH Keywords: real spectrum
zbMATH Keywords: finitely generated groups
zbMATH Keywords: hyperbolic structures
zbMATH Keywords: real compactification
zbMATH Keywords: boundary points
MaRDI profile type: Publication
OpenAlex ID: W1998892340
cites work: Length functions of group actions on \(\Lambda\)-trees
cites work: Q3810928
cites work: Q3805387
cites work: Q3770650
cites work: Normal spectral spaces and their dimensions
cites work: Q4191989
cites work: Diskrete Untergruppen von \(SL_2 (R)\).
cites work: Group actions on trees and the compactification of the space of classes of SO(n,1)-representations
cites work: Λ-trees and their applications
cites work: Valuations, trees, and degenerations of hyperbolic structures. I
cites work: The invariant theory of \(n\times n\) matrices
cites work: Affine coordinates for Teichmüller spaces
cites work: Invariant theory
cites work: Q3203300
cites work: Triangulations of Subanalytic Sets and Locally Subanalytic Manifolds
cites work: Discrete Moebius Groups: Fundamental Polyhedra and Convergence
DOI: 10.5802/AIF.1401
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published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 672144