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
MSP Books and Monographs
About this Series
Editorial Board
Ethics Statement
Author Index
Submission Guidelines
Author Copyright Form
Purchases
ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
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 ρn of the fundamental group of a closed hyperbolic 3–manifold fibering over the circle into the isometry group Iso 4 of the hyperbolic space 4. The algebraic limit of ρn contains a finitely generated subgroup F whose 3–dimensional quotient Ω(F)F has infinitely generated fundamental group, where Ω(F) is the discontinuity domain of F acting on the sphere at infinity S3 = 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
References
Publication
Received: 20 November 1997
Revised: 7 November 1998
Published: 17 November 1998
Authors
Leonid Potyagailo
Département de Mathématiques
Université de Lille 1
59655 Villeneuve d’Ascq
France