Graph manifolds, ends of negatively curved spaces and the hyperbolic 120- cell space. (English) Zbl 0777.53035

In this paper complete Riemannian manifolds of finite volume with negative sectional curvature uniformly bounded from below whose ends consist of certain graph manifolds are constructed. These results rely on detailed curvature computations for a modification of the hyperbolic metric on a 4-dimensional hyperbolic space form where certain surfaces are removed. To satisfy the assumptions of the metric construction the fundamental domain for a particular cocompact arithmetic group is determined. Here the hyperbolic 120-cell, mentioned in the title, comes in.


53C20 Global Riemannian geometry, including pinching
57S25 Groups acting on specific manifolds
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