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The visual core of a hyperbolic 3-manifold

By James W. Anderson and Richard D. Canary

Abstract

In this note we introduce the notion of the visual core of a hyperbolic 3-manifold N, and explore some of its basic properties. We investigate circumstances under which the visual core V(N') of a cover N' of N embeds in N, via the usual covering map. We go on to show that if the algebraic limit of a sequence of isomorphic Kleinian groups is a generalized web group, then the visual core of the algebraic limit manifold embeds in the geometric limit manifold. Finally, we discuss the relationship between the visual core and Klein-Maskit combination along component subgroups

Topics: QA
Year: 2001
OAI identifier: oai:eprints.soton.ac.uk:29873
Provided by: e-Prints Soton

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Citations

  1. (1969). Ahlfors, “The structure of a finitely generated Kleinian group,”
  2. (1990). Algebraic and geometric convergence of Kleinian groups,”
  3. (1996). Algebraic limits of Kleinian groups which rearrange the pages of a book,”
  4. (1987). Convex hulls in hyperbolic spaces, a theorem of Sullivan, and measured pleated surfaces,” in Analytical and Geometrical Aspects of Hyperbolic Spaces,
  5. (1996). Cores of hyperbolic 3-manifolds and limits of Kleinian groups,”
  6. (1993). Ends of hyperbolic 3-manifolds,”
  7. (1996). Free Kleinian groups and volumes of hyperbolic 3-manifolds,”
  8. (1992). Function groups in Kleinian groups,”
  9. Geometrical finiteness for hyperbolic groups,”
  10. (1988). Kleinian groups,
  11. (1970). On boundaries of Teichm¨ uller spaces and on Kleinian groups II,”
  12. (1984). On Thurston’s uniformization theorem for three-dimensional manifolds,” in The Smith Conjecture,

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