Abstract
Long and Reid [Algebr. Geom. Topol. 2: 285–296, 2002] have shown that the diffeomorphism class of every Riemannian flat manifold of dimension n≥ 3 arises as a cusp cross-section of a complete finite volume real hyperbolic (n+1)-orbifold. For the complex hyperbolic case, McReynolds [Algebr. Geom. Topol. 4: 721–755, 2004] proved that every 3-dimensional infranilmanifold is diffeomorphic to a cusp cross-section of a complete finite volume complex hyperbolic 2-orbifold. Moreover, he gave a necessary and sufficient condition for a Heisenberg infranilmanifold to be realized as a cusp cross-section of finite volume (arithmetically) complex hyperbolic orbifold. We study these realization problems by using Seifert fibrations.
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Kamishima, Y. Cusp Cross-Sections of Hyperbolic Orbifolds by Heisenberg Nilmanifolds I. Geom Dedicata 122, 33–49 (2006). https://doi.org/10.1007/s10711-006-9049-0
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DOI: https://doi.org/10.1007/s10711-006-9049-0
Keywords
- Real
- Complex hyperbolic manifold
- Flat manifold
- Finite volume
- Heisenberg infranilmanifold
- Cusp cross-section
- Group extension
- Seifert fibration