Cusps, triangle groups and hyperbolic 3-folds

Journal of the Australian Mathematical Society

Marston D. E. Conder¹ 

[1] Gaven J. Martin

关键词: 20 H 10;    30 F 40;    57 N 10;   

DOI  :  10.1017/S1446788700032018

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

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.

【 授权许可】

Unknown