Maximal Holonomy of Almost Bieberbach Groups for Heis5 |
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| Authors: | Kyung Bai Lee Andrzej Szczepański |
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| Institution: | (1) University of Oklahoma, Norman, OK, 73019, U.S.A.;(2) Institute of Mathematics, University of Gda sk, ul.Wita Stwosza 57, 80–952 Gdask, Poland |
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| 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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| Keywords: | almost Bieberbach group holonomy group Heisenberg group complex hyperbolic manifold |
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