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Theses

Representations of fundamental groups in hyperbolic geometry

Abstract : Two construction methods of group representations are presented. The first one proposes a strategy to try to determine the representations of finitely generated free groups into any lattice in real Lie groups. The second, after reviewing a construction of a complex hyperbolic surface, that is the quotient of the complex hyperbolic plane by a lattice, and examining its properties carefully, yields infinitely many non-conjugate representations into a lattice in the group of isometries of the complex hyperbolic plane, of fundamental groups of closed hyperbolic 3-dimensional manifolds, obtained as surface bundles over the circle.
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Ruben Dashyan. Representations of fundamental groups in hyperbolic geometry. General Mathematics [math.GM]. Université Pierre et Marie Curie - Paris VI, 2017. English. ⟨NNT : 2017PA066242⟩. ⟨tel-01684245⟩

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