Traces, Cross-Ratios and 2-Generator Subgroups of SU(2, 1)

Will, Pierre

Canadian journal of mathematics, Tome 61 (2009) no. 6, pp. 1407-1436

Résumé

In this work, we investigate how to decompose a pair $\left( A,\,B \right)$ of loxodromic isometries of the complex hyperbolic plane $\mathbf{H}_{\mathbb{C}}^{2}$ under the form $A\,=\,{{I}_{1}}{{I}_{2}}$ and $B\,=\,{{I}_{3}}{{I}_{2}}$ , where the ${{I}_{k}}$ 's are involutions. The main result is a decomposability criterion, which is expressed in terms of traces of elements of the group $\left\langle A,\,B \right\rangle $ .

Détail

DOI : 10.4153/CJM-2009-067-6

Mots-clés : 14L24, 22E40, 32M15, 51M10

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