Abstract
Let Heis 2n+1 be the Heisenberg group of dimension 2n + 1 and M an infra-nilmanifold with Heis 2n+1-geometry. The fundamental group of M contains a cocompact lattice of Heis 2n+1 with index bounded above by a universal constant I n+1, i.e., I n+1 is the maximal order of the holonomy groups. We prove that I 3 = 24. As an application we give an estimate for the volumes of finite volume non-compact complex hyperbolic 3-manifolds.
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Lee, K.B., Szczepański, A. Maximal Holonomy of Almost Bieberbach Groups for Heis5. Geometriae Dedicata 87, 167–180 (2001). https://doi.org/10.1023/A:1012032913680
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DOI: https://doi.org/10.1023/A:1012032913680