The Geometry of the Eisenstein-picard Modular Group
نویسنده
چکیده
The Eisenstein-Picard modular group PU(2, 1;Z[ω]) is defined to be the subgroup of PU(2, 1) whose entries lie in the ring Z[ω], where ω is a cube root of unity. This group acts isometrically and properly discontinuously on H C , that is, on the unit ball in C2 with the Bergman metric. We construct a fundamental domain for the action of PU(2, 1;Z[ω]) on H2 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 PU(2, 1).
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