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A Note on Quaternionic Hyperbolic Ideal Triangle Groups
Published online by Cambridge University Press: 20 November 2018
Abstract
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In this paper, the quaternionic hyperbolic ideal triangle groups are parametrized by a real one-parameter family
$\{{{\phi }_{s}}\,:\,s\,\in \,\mathbb{R}\}$
. The indexing parameter s is the tangent of the quaternionic angular invariant of a triple of points in
$\partial \mathbf{H}_{\mathbb{H}}^{2}$
forming this ideal triangle. We show that if
$s>\sqrt{125/3},$
then
${{\phi }_{S}}$
is not a discrete embedding, and if
$s\,\le \,\sqrt{3\text{5}}$
, then
${{\phi }_{S}}$
is a discrete embedding.
Keywords
- Type
- Research Article
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- Copyright © Canadian Mathematical Society 2016
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