Cusp cross-sections of hyperbolic orbifolds by Heisenberg nilmanifolds. I
type: Item
instance of: scholarly article
title: Cusp cross-sections of hyperbolic orbifolds by Heisenberg nilmanifolds. I
zbMATH Open document ID: 1123.53018
author: Yoshinobu Kamishima
published in: Geometriae Dedicata
publication date: 2007-05-18T00:00:00Z
review text: Let \(\pi\) be a \textbf{K}-Heisenberg crystallographic group with group extension \(1\to \Delta\to \pi\to Q\) where \(\Delta\) is a maximal normal nilpotent subgroup and \(Q\) is a finite subgroup. By using the Seifert fibration, the author gives a discrete faithful representation of the \textbf{K}-Heisenberg crystallographic group, which is stated as follows: Theorem. There exists an injective homomorphism \(\mathcal{A}:\pi\rightarrow \Delta\rtimes \Aut\;\Delta\). Then the author uses this theorem to study the realization problem of Riemannian flat manifolds and Heisenberg infranilmanifolds. The author gives another proof of a result of \textit{D. D. Long} and \textit{A. W. Reid} on compact Riemannian flat orbifolds [Algebr. Geom. Topol. 2, 285--296 (2002; Zbl 0998.57038)]. In addition, the author also gives a generalization of \textit{D. B. McReynold}'s result on Heisenberg infranilmanifolds [Algebr. Geom. Topol. 4, 721--755 (2004; Zbl 1058.57012)].
reviewed by: Zhi Lü
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 51M10
zbMATH DE Number: 5154818
zbMATH Keywords: real (complex) hyperbolic manifold
zbMATH Keywords: flat manifold
zbMATH Keywords: finite manifold
zbMATH Keywords: Heisenberg infranilmanifold
zbMATH Keywords: cusp cross-section
zbMATH Keywords: group extension
zbMATH Keywords: Seifert fibration
MaRDI profile type: Publication
full work available at URL: s10711-006-9049-0
OpenAlex ID: W2033111095
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DOI: 10.1007/S10711-006-9049-0
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description: scientific article; zbMATH DE number 5154818