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Primitive stable representations of geometrically infinite handlebody hyperbolic 3-manifolds. (Représentations primitivement stables des variétés hyperboliques géométriquement infinies du bretzel creux.) (English. Abridged French version) Zbl 1206.57022
Authors’ abstract: We show that a discrete and faithful representation of a free group in $$PSL(2, {\mathbb{C}})$$ without parabolics is primitive stable.

##### MSC:
 57N10 Topology of general $$3$$-manifolds (MSC2010) 57M50 General geometric structures on low-dimensional manifolds 30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
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##### References:
 [1] Agol, I., Tameness of hyperbolic 3-manifolds, (2004), preprint [2] B. Bowditch, Geometric model for hyperbolic manifolds, Southhampton, 2005, preprint. [3] Calegari, D.; Gabai, D., Shrinkwrapping and the taming of hyperbolic 3-manifolds, J. amer. math. soc., 19, 2, 385-446, (2006) · Zbl 1090.57010 [4] Canary, R.D., Ends of hyperbolic 3-manifolds, J. amer. math. soc., 6, 1, 1-35, (1993) · Zbl 0810.57006 [5] Das, S.; Mj, M., Addendum to ending laminations and Cannon-Thurston maps: parabolics, (2010), preprint [6] Floyd, W.J., Group completions and limit sets of Kleinian groups, Invent. math., 57, 205-218, (1980) · Zbl 0428.20022 [7] Jeon, W.; Kim, I., On primitive stable representations of geometrically infinite handlebody hyperbolic 3-manifolds, (2010), preprint [8] Kim, I., Divergent sequences of function groups, Differential geom. appl., 26, 6, 645-655, (2008) · Zbl 1166.58008 [9] Kim, I.; Lecuire, C.; Ohshika, K., Convergence of freely decomposable Kleinian groups, (2004), preprint [10] Minsky, Y., On dynamics of $$\mathit{Out}(F_n)$$ on $$\mathit{PSL}_2(\mathbb{C})$$ characters, (2009), preprint [11] Mj, M., Cannon-Thurston maps for Kleinian groups, (2010), preprint · Zbl 1370.57008 [12] J.-P. Otal, Courants géodésiques et produits libres, Thèse d’Etat, Université de Paris-Sud, Orsay, 1988. [13] J.R. Stallings, Whitehead graphs on handlebodies, 1996, preprint. [14] Whitehead, J.H.C., On certain sets of elements in a free group, Proc. London math. soc., 41, 48-56, (1936) · JFM 62.0079.04 [15] Whitehead, J.H.C., On equivalent sets of elements in a free group, Ann. of math., 37, 780-782, (1936)
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