Quaternions and some global properties of hyperbolic 5-manifolds

We provide an explicit thick and thin decomposition for oriented hyperbolic manifolds M of dimension 5. The result implies improved universal lower bounds for the volume vol(5)(M) and, for M compact, new estimates relating the injectivity radius and the diameter of M with vol(5) (M). The quantification of the thin part is based upon the identification of the isometry group of the universal space by the matrix group PSDelta L(2, H) of quaternionic 2 x 2-matrices with Dieudonne determinant A equal to 1 and isolation properties of PSDelta L(2, H).