Geometry and Markoff's spectrum for \(\mathbb{Q}(i)\). I (Q2849041)
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scientific article; zbMATH DE number 6208250
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Geometry and Markoff's spectrum for \(\mathbb{Q}(i)\). I |
scientific article; zbMATH DE number 6208250 |
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16 September 2013
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Markoff's spectrum
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Geometry and Markoff's spectrum for \(\mathbb{Q}(i)\). I (English)
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\textit{H. Cohn} [Acta Arith. 18, 125--136 (1971; Zbl 0218.10041)] studied the relation between Markoff's spectrum for the rational number field \(\mathbb{Q}\) and the Euclidean height of geodesics given by primitive elements of a two generator subgroup in \(\text{PSL}(2,\mathbb{R})\). The quotient space of the hyperbolic plane \(\mathbb{H}^2\) by this subgroup is a once punctured torus.NEWLINENEWLINEIn the paper under review, the authors study the relation between Markoff's spectrum for the imaginary quadratic number field \(\mathbb{Q}(i)\) and the Euclidean height of geodesics of certain elements of a subgroup in \(\text{PSL}(2,\mathbb{C})\). The quotient space of the hyperbolic space \(\mathbb{H}^3\) by this subgroup is the Borromean rings complement.
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