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Mathematical Research Letters 8, 113 (2001) CONSTRUCTING HYPERBOLIC MANIFOLDS WHICH
 

Summary: Mathematical Research Letters 8, 113 (2001)
CONSTRUCTING HYPERBOLIC MANIFOLDS WHICH
BOUND GEOMETRICALLY
D. D. Long1
and A. W. Reid2
1. Introduction
Let Hn
denote hyperbolic n-space, that is the unique connected simply con-
nected Riemannian manifold of constant curvature -1. By a hyperbolic n-
orbifold we shall mean a quotient Hn
/ where is a discrete group of isome-
tries of Hn
. If a hyperbolic n-manifold M is the totally geodesic boundary of a
hyperbolic (n + 1)-manifold W, we will say that M bounds geometrically. It was
shown in [11] that if a closed orientable hyperbolic M4k-1
bounds geometrically,
then (M4k-1
) Z. Closed hyperbolic 3-manifolds with integral eta are fairly
rare for example, of the 11, 000 or so manifolds in the census of small volume
closed hyperbolic 3-manifolds, computations involving Snap (see [3]) rule out all

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics