The canonical decompositions of some family of compact orientable hyperbolic 3-manifolds with totally geodesic boundary
type: Item
instance of: scholarly article
title: The canonical decompositions of some family of compact orientable hyperbolic 3-manifolds with totally geodesic boundary
zbMATH Open document ID: 0937.57014
DOI: 10.1023/A:1005181102798
author: Akira Ushijima
published in: Geometriae Dedicata
publication date: 2000-05-30T00:00:00Z
review text: \textit{L. Paoluzzi} and \textit{B. Zimmermann} [ibid. 60, No. 2, 113-123 (1996; Zbl 0857.57009)] constructed and topologically classified a family of compact orientable hyperbolic 3-manifolds with totally geodesic boundaries. The author determines the canonical decomposition by truncated ideal polyhedra of these manifolds in the sense of \textit{D. B. A. Epstein} and \textit{R. C. Penner} [J. Differ. Geom. 27, No. 1, 67-80 (1988; Zbl 0611.53036)] as extended by \textit{S. Kojima} [Adv. Stud. Pure Math. 20, 93-112 (1992; Zbl 0802.57006)]. This is used to give a new proof of the topological classification, as well as to determine the isometry groups and volumes of the Paoluzzi- Zimmermann manifolds. These manifolds include the exteriors of \textit{S. Suzuki}'s Brunnian graphs [Kobe J. Math. 1, 19-22 (1984; Zbl 0565.57008)]. Thereby, the author obtains new information about the chirality and symmetry groups of these graphs.
reviewed by: Bruce Hughes
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 1383253
zbMATH Keywords: hyperbolic 3-manifold
zbMATH Keywords: polyhedral canonical decomposition
zbMATH Keywords: Suzuki's Brunnian graph
zbMATH Keywords: Heegaard splitting
MaRDI profile type: Publication
full work available at URL: a:1005181102798
OpenAlex ID: W96028503
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description: scientific article; zbMATH DE number 1383253