The canonical decompositions of some family of compact orientable hyperbolic 3-manifolds with totally geodesic boundary
\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.
scientific article; zbMATH DE number 1383253