Geometry & Topology Monographs 1 (1998),
The Epstein Birthday Schrift,
paper no. 23, pages 479-492.
The boundary of the deformation space of the fundamental
group of some hyperbolic 3-manifolds fibering over the circle
Leonid Potyagailo
Abstract.
By using Thurston's bending construction we obtain a sequence of
faithful discrete representations \rho _n of the fundamental group of
a closed hyperbolic 3-manifold fibering over the circle into the
isometry group Iso H^4 of the hyperbolic space H^4. The algebraic
limit of \rho _n contains a finitely generated subgroup F whose
3-dimensional quotient \Omega (F)/F has infinitely generated
fundamental group, where \Omega (F) is the discontinuity domain of F
acting on the sphere at infinity. Moreover F is isomorphic to the
fundamental group of a closed surface and contains infinitely many
conjugacy classes of maximal parabolic subgroups.
Keywords. Discrete (Kleinian) subgroups, deformation
spaces, hyperbolic 4-manifolds, conformally flat 3-manifolds, surface
bundles over the circle
AMS subject classification.
Primary: 57M10, 30F40, 20H10. Secondary: 57S30, 57M05, 30F10, 30F35.
E-print: arXiv:math.GT/9811181
Submitted: 20 November 1997.
(Revised: 7 November 1998.)
Published: 17 November 1998.
Notes on file formats
Leonid Potyagailo
Departement de Mathematiques
Universite de Lille 1
59655 Villeneuve d'Ascq, France
Email: potyag@gat.univ-lille1.fr
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