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Small hyperbolic 3-manifolds with geodesic boundary. (English) Zbl 1068.57012

The authors classify the orientable finite-volume hyperbolic 3-manifolds having nonempty compact totally geodesic boundary and admitting an ideal triangulation with at most four tetrahedra. They also compute the volume of all such manifolds, describe their canonical Kojima decomposition, and discuss manifolds having cusps.

MSC:

57M50 General geometric structures on low-dimensional manifolds
57M20 Two-dimensional complexes (manifolds) (MSC2010)
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
57M10 Covering spaces and low-dimensional topology

Software:

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References:

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