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Soit $r$ un entier $> 1$ . Une 3-variété $M$ est dite $r$ -périodique si et seulement si le groupe cyclique $G = ℤ / r ℤ$ agit semi-librement sur $M$ avec un cercle comme l’ensemble des points fixes. Dans cet article, nous utilisons les invariants quantiques $θ_{p}$ pour établir des conditions nécessaires pour qu’une 3-variété soit périodique.

Limit sets of free convergence groups.

Isachenko, N.A. (2002)

Sibirskij Matematicheskij Zhurnal

Local coordinates for $SL (n, C)$ -character varieties of finite-volume hyperbolic 3-manifolds

Pere Menal-Ferrer, Joan Porti (2012)

Annales mathématiques Blaise Pascal

Given a finite-volume hyperbolic 3-manifold, we compose a lift of the holonomy in $SL (2, C)$ with the $n$ -dimensional irreducible representation of $SL (2, C)$ in $SL (n, C)$ . In this paper we give local coordinates of the $SL (n, C)$ -character variety around the character of this representation. As a corollary, this representation is isolated among all representations that are unipotent at the cusps.

Local rigidity of aspherical three-manifolds

Pierre Derbez (2012)

Annales de l’institut Fourier

In this paper we construct, for each aspherical oriented $3$ -manifold $M$ , a $2$ -dimensional class in the $l_{1}$ -homology of $M$ whose norm combined with the Gromov simplicial volume of $M$ gives a characterization of those nonzero degree maps from $M$ to $N$ which are homotopic to a covering map. As an application we characterize those degree one maps which are homotopic to a homeomorphism in term of isometries between the bounded cohomology groups of $M$ and $N$ .

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