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The visual core of a hyperbolic 3-manifold

The visual core of a hyperbolic 3-manifold
The visual core of a hyperbolic 3-manifold
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.
0025-5831
989-1000
Anderson, James W.
739c0e33-ef61-4502-a675-575d08ee1a98
Canary, Richard D.
a26b9c05-b5d3-4837-a48e-0e7bb788c0b9
Anderson, James W.
739c0e33-ef61-4502-a675-575d08ee1a98
Canary, Richard D.
a26b9c05-b5d3-4837-a48e-0e7bb788c0b9

Anderson, James W. and Canary, Richard D. (2001) The visual core of a hyperbolic 3-manifold. Mathematische Annalen, 321 (4), 989-1000. (doi:10.1007/s002080100269).

Record type: Article

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.

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Published date: December 2001

Identifiers

Local EPrints ID: 29873
URI: https://eprints.soton.ac.uk/id/eprint/29873
ISSN: 0025-5831
PURE UUID: c4bf80ed-b0e8-496d-96f3-495d61e61070
ORCID for James W. Anderson: ORCID iD orcid.org/0000-0002-7849-144X

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Date deposited: 11 May 2006
Last modified: 06 Jun 2018 13:03

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