#### Volume 1 (1998)

 Recent Volumes Volume 1, 1998 Volume 2, 1999 Volume 3, 2000 Volume 4, 2002 Volume 5, 2002 Volume 6, 2003 Volume 7, 2004 Volume 8, 2006 Volume 9, 2006 Volume 10, 2007 Volume 11, 2007 Volume 12, 2007 Volume 13, 2008 Volume 14, 2008 Volume 15, 2008 Volume 16, 2009 Volume 17, 2011 Volume 18, 2012 Volume 19, 2015
 The Series About this Series Ethics Statement Purchase Printed Copies Author Index ISSN (electronic): 1464-8997 ISSN (print): 1464-8989 MSP Books and Monographs Other MSP Publications
The boundary of the deformation space of the fundamental group of some hyperbolic 3–manifolds fibering over the circle

### Leonid Potyagailo

Geometry & Topology Monographs 1 (1998) 479–492
DOI: 10.2140/gtm.1998.1.479
 arXiv: math.GT/9811181
##### Abstract
[an error occurred while processing this directive]

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 $\Omega \left(F\right)∕F$ has infinitely generated fundamental group, where $\Omega \left(F\right)$ is the discontinuity domain of $F$ acting on the sphere at infinity ${S}_{\infty }^{3}=\partial {ℍ}^{4}$. 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
##### Mathematical Subject Classification
Primary: 57M10, 30F40, 20H10
Secondary: 57S30, 57M05, 30F10, 30F35