Maximal Symmetry Groups of Hyperbolic three-manifolds
Conder, Marsten; Martin, Gaven; Torstensson, Anna (2006). Maximal Symmetry Groups of Hyperbolic three-manifolds. New Zealand Journal of Mathematics, 35, (1), 37 - 62
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Published
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English
Authors:
Conder, Marsten
;
Martin, Gaven
;
Torstensson, Anna
Department:
Mathematics (Faculty of Engineering)
Algebra
Abstract:
Every nite group acts as the full isometry group of some compact hyperbolic 3-manifold. In this paper we study those nite groups which act maximally, that is when the ratio jIsom+(M)j=vol(M)is maximal among all such manifolds. In two dimensions maximal symmetry groups are called Hurwitz groups, and arise as quotients of the (2,3,7){triangle group. Here
we study quotients of the minimal co-volume lattice.
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