A note on quaternionic hyperbolic ideal triangle groups. (Q2810703)
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scientific article; zbMATH DE number 6589341
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on quaternionic hyperbolic ideal triangle groups. |
scientific article; zbMATH DE number 6589341 |
Statements
3 June 2016
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quaternionic inversion
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quaternionic hyperbolic ideal triangle groups
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quaternionic Cartan angular invariants
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free products of cyclic groups
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A note on quaternionic hyperbolic ideal triangle groups. (English)
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Let \(\Gamma=\langle a_1,a_2,a_3\mid a^2_1=a^2_2=a^2_3=1\rangle\) be the free product of three cyclic groups of order two. A complex hyperbolic ideal triangle group is a representation \(\phi_s\colon\Gamma\to\mathrm{PU}(2,1)\). The character space of \(\Gamma\) is then described by the one parameter \(s\) which represents the trace of the image of \(a_1a_2a_3\). If \(s\leq\sqrt{35}\) then \(\phi_s(\Gamma)\) is discrete whereas \(\phi_s(\Gamma)\) is not discrete if \(s>\sqrt{125/3}\).
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