Algorithms, complexity and discreteness criteria in \(PSL(2,C)\) (Q1385406)

In the paper, the discreteness problem for subgroups of \(\text{PSL}(2,\mathbb{C})\) is studied. As the main result the computational complexity of the rational number algorithm for \(\text{PSL}(2,\mathbb{Q})\), the real number algorithm for \(\text{PSL}(2,\mathbb{R})\), and the Turing machine algorithm for \(\text{PSL}(2, \mathbb{Q}(\gamma))\) is determined. Also the computational complexity of Riley's \(\text{PSL}(2,\mathbb{C})\) procedure and Jørgenson's inequality is investigated.