The geometry of the Eisenstein-Picard modular group
The geometry of the Eisenstein-Picard modular group
复制标题
Eisenstein-Picard模群的几何
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
J. Parker
中科院分区：
文献类型：
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作者：
E. Falbel;J. Parker
The Eisenstein-Picard modular group ${
m PU}(2,1;mathbb {Z}[omega])$ is defined to be the subgroup of ${
m PU}(2,1)$ whose entries lie in the ring $mathbb {Z}[omega]$, where $omega$ is a cube root of unity. This group acts isometrically and properly discontinuously on ${f H}^2_mathbb{C}$, that is, on the unit ball in $mathbb {C}^2$ with the Bergman metric. We construct a fundamental domain for the action of ${
m PU}(2,1;mathbb {Z}[omega])$ on ${f H}^2_mathbb {C}$, which is a 4-simplex with one ideal vertex. As a consequence, we elicit a presentation of the group (see Theorem 5.9). This seems to be the simplest fundamental domain for a finite covolume subgroup of ${
m PU}(2,1)$
The Eisenstein-Picard modular group ${
m PU}(2,1;mathbb {Z}[omega])$ is defined to be the subgroup of ${
m PU}(2,1)$ whose entries lie in the ring $mathbb {Z}[omega]$, where $omega$ is a cube root of unity. This group acts isometrically and properly discontinuously on ${f H}^2_mathbb{C}$, that is, on the unit ball in $mathbb {C}^2$ with the Bergman metric. We construct a fundamental domain for the action of ${
m PU}(2,1;mathbb {Z}[omega])$ on ${f H}^2_mathbb {C}$, which is a 4-simplex with one ideal vertex. As a consequence, we elicit a presentation of the group (see Theorem 5.9). This seems to be the simplest fundamental domain for a finite covolume subgroup of ${
m PU}(2,1)$