论文标题
单张比安奇小组的演讲
Presentations for Singly-Cusped Bianchi Groups
论文作者
论文摘要
我们制作了单个Bianchi组的组演示文稿的完整列表，$ PSL_2（\ Mathcal {o} _d）$其中$ \ Mathcal {o} _d $是$ \ Mathbb {q}（Q}（Q}（\ sqrt {d} {d}）$ d $ d $ d $ d $ d $ -11， - -1， - -1， - -2， - -2， - -2， - -2， - -2， - -2， - 3， - 3， - 3， - sqrt {q}， - -2， - 3 -43，-67或-163。为此，由于Macbeath，我们将一个定理应用于一个足够大的Horoball，将Bianchi组作为$ \ Mathbf {H}^3 $的异构体的离散子组。据我们所知，当$ D $为-43，-67或-163时，以前不知道明确的演示文稿。
We produce a complete list of group presentations for singly-cusped Bianchi groups, $PSL_2 (\mathcal{O}_d)$ where $\mathcal{O}_d$ is the ring of integers for $\mathbb{Q}(\sqrt{d})$ and $d$ is -1, -2, -3, -7, -11, -19, -43, -67, or -163. To do this, we apply a theorem due to Macbeath to a sufficiently large horoball, treating the Bianchi groups as discrete subgroups of isometries for $\mathbf{H}^3$. As far as we know, explicit presentations were not previously known when $d$ is -43, -67, or -163.
