J Austral Math Soc Ser A 55 pp149--182, 1993.

Cusps, Triangle Groups ad Hyperbolic 3-Folds

Marston D. E. Conder and Gaven J. Martin

Abstract

We provide a number of explicit examples of small volume hyperbolic 3-manifolds and 3-orbifolds with various geometric properties. These include a sequence of orbifolds with torsion of order q interpolating between the smallest volume cusped orbifold (q = 6) and the smallest volume limit orbifold (q ® ¥), hyperbolic 3-manifolds with automorphism groups with large orders in relation to volume and in arithmetic progression, and the smallest volume hyperbolic manifolds with totally geodesic surfaces. In each case we provide a presentation for the associated Kleinian group and exhibit a fundamental domain and an integral formula for the co-volume. We discuss other interesting properties of these groups.

1991 AMS Subject Classification: 20H10, 30F40, 57N10

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Authors

Marston D. E. Conder

Department of Mathematics, The University of Auckland, Private Bag 92019 Auckland, NEW ZEALAND.

mailto:conder@mat.aukuni.ac.nz

Gaven J. Martin

Department of Mathematics, The University of Auckland, Private Bag 92019 Auckland, NEW ZEALAND.

mailto:martin@mat.aukuni.ac.nz