Mathematics – Geometric Topology
Scientific paper
2011-07-28
Mathematics
Geometric Topology
26 pages, 15 figures
Scientific paper
We bound two global invariants of cusped hyperbolic manifolds: the length of the shortest closed geodesic (the systole), and the radius of the biggest embedded ball (the inradius). We give an upper bound for the systole, expressed in terms of the dimension and simplicial volume. We find a positive lower bound on the inradius independent of the dimension. These bounds are sharp in dimension 3, realized by the Gieseking manifold. It provides a new characterization of this manifold.
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