 
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 nspace, 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 nmanifold 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 M4k1
bounds geometrically,
then (M4k1
) Z. Closed hyperbolic 3manifolds with integral eta are fairly
rare for example, of the 11, 000 or so manifolds in the census of small volume
closed hyperbolic 3manifolds, computations involving Snap (see [3]) rule out all
