Groupes triangulaires lagrangiens en géométrie hyperbolique complexe
Pierre Will1
1 Université Pierre et Marie Curie Institut de Mathématiques 4 place Jussieu 75252 Paris cedex 05 (France)
Séminaire de théorie spectrale et géométrie, Volume 25 (2006-2007), pp. 189-209.

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.

Nous présentons quelques résultats au sujet des groupes engendrés par trois involutions antiholomorphes dans le cadre du plan hyperbolique complexe H ℂ 2 .

DOI: 10.5802/tsg.256
Classification: 32G15, 32M15, 32Q45, 57S30
Pierre Will 1

1 Université Pierre et Marie Curie Institut de Mathématiques 4 place Jussieu 75252 Paris cedex 05 (France) 
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Pierre Will. Groupes triangulaires lagrangiens en géométrie hyperbolique complexe. Séminaire de théorie spectrale et géométrie, Volume 25 (2006-2007), pp. 189-209. doi : 10.5802/tsg.256. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.256/

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