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Discrete parabolic representations of link groups

Published online by Cambridge University Press:  26 February 2010

Robert Riley
Robert Riley
Affiliation:
The University of Southampton, Southampton SO9 5NH, England
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Let k be a knot of type K and with group πK. Let θ: nK → PSL(ℂ) = PSL (2, ℂ) be a parabolic representation (p-rep) as defined in [14]. We shall call the representation discrete when its image πKθ is a discrete subgroup of PSL(ℂ). It is known that PSL(ℂ) can be identified with the group of orientation preserving isometries of hyperbolic 3-space , and that each discrete subgroup of PSL(ℂ) acts discontinuously on . Hence each discrete p-rep θ has an associated orbit space . The present paper is a study of the general relations between the algebraic properties of a discrete image πKθ and the geometric properties of its orbit space.

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Type
Research Article
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Mathematika , Volume 22 , Issue 2 , December 1975 , pp. 141 - 150
Copyright
Copyright © University College London 1975

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