Torsion de Reidemeister pour les Varietes Hyperboliques

Defines and studies a Reidemeister torsion for hyperbolic three-dimensional manifolds of finite volume. This work includes examples and studies the main properties, involving many aspects of hyperbolic three-manifolds. It also shows that the torsion of hyperbolic cone manifolds tends to zero for Euclidean degenerations.

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In this work, the author defines and studies a Reidemeister torsion for hyperbolic three-dimensional manifolds of finite volume. This torsion is an invariant obtained from the combinatorial and the hyperbolic structures of the manifold, and it is studied for closed manifolds and orbifolds, cusped and cone manifolds. The author includes several examples and studies the main properties, involving many aspects of hyperbolic three-manifolds. In particular, it is shown that the torsion of hyperbolic cone manifolds tends to zero for Euclidean degenerations. This work features the text in French.