Groupes triangulaires lagrangiens en géométrie hyperbolique complexe

Pierre Will[1]

  • [1] Université Pierre et Marie Curie Institut de Mathématiques 4 place Jussieu 75252 Paris cedex 05 (France)

Séminaire de théorie spectrale et géométrie (2006-2007)

  • Volume: 25, page 189-209
  • ISSN: 1624-5458

Abstract

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There is still much to learn about discrete subgroups of PU( n ,1), the group of holomorphic isometries of the complex hyperbolic n-space. Given a finitely generated group G, describing the discrete and faithful representation of G into PU( n ,1) is a difficult task, which has been carried out in only few cases. In this note we expose some results about Lagrangian triangle groups in the frame of PU(2,1). These groups are generated by three antiholomorphic isometric involutions. They are connected to many of the known examples of discrete subgroups of PU(2,1). The main result stated here is the existence of a one parameter family of embeddings of the Teichmueller space of the once punctured torus into the PU(2,1)-representation variety of the free group of rank two. These embeddings are described using Lagrangian triangle groups.

How to cite

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Will, Pierre. "Groupes triangulaires lagrangiens en géométrie hyperbolique complexe." Séminaire de théorie spectrale et géométrie 25 (2006-2007): 189-209. <http://eudml.org/doc/11225>.

@article{Will2006-2007,
abstract = {Nous présentons quelques résultats au sujet des groupes engendrés par trois involutions antiholomorphes dans le cadre du plan hyperbolique complexe $\mathbf\{H\}^\{2\}_\{\mathbb\{C\}\}$.},
affiliation = {Université Pierre et Marie Curie Institut de Mathématiques 4 place Jussieu 75252 Paris cedex 05 (France)},
author = {Will, Pierre},
journal = {Séminaire de théorie spectrale et géométrie},
language = {fre},
pages = {189-209},
publisher = {Institut Fourier},
title = {Groupes triangulaires lagrangiens en géométrie hyperbolique complexe},
url = {http://eudml.org/doc/11225},
volume = {25},
year = {2006-2007},
}

TY - JOUR
AU - Will, Pierre
TI - Groupes triangulaires lagrangiens en géométrie hyperbolique complexe
JO - Séminaire de théorie spectrale et géométrie
PY - 2006-2007
PB - Institut Fourier
VL - 25
SP - 189
EP - 209
AB - Nous présentons quelques résultats au sujet des groupes engendrés par trois involutions antiholomorphes dans le cadre du plan hyperbolique complexe $\mathbf{H}^{2}_{\mathbb{C}}$.
LA - fre
UR - http://eudml.org/doc/11225
ER -

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