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Groupes libres, groupes triangulaires et tore épointé dans PU(2,1)

Abstract : The main theme in this work is the study of representations of
surface groups in the real non-compact Lie group PU(2,1), which is the isometry
group of the complex hyperbolic plane. More precisely, we are
interested in the representations of the fundamental group of the once
punctured torus in PU(2,1). Our main
result states the existence of a 3 parameter family of discrete,
faithful an type preserving representations of the punctured torus
fundamental group in PU(2,1). The main tool in the proof is a new
type of hypersurface of the complex hyperbolic plane, which we use to build
fondamental domains. We also study the decomposability of
representations, and give criteria to guaranty the existence of a
decomposition, both in terms of traces and cross ratios.
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Contributor : Pierre Will Connect in order to contact the contributor
Submitted on : Tuesday, February 13, 2007 - 6:37:27 PM
Last modification on : Sunday, June 26, 2022 - 5:18:57 AM
Long-term archiving on: : Tuesday, April 6, 2010 - 11:53:38 PM



  • HAL Id : tel-00130785, version 1


Pierre Will. Groupes libres, groupes triangulaires et tore épointé dans PU(2,1). Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2006. Français. ⟨tel-00130785⟩



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