Geodesic
Quaternions and Some Global Properties of Hyperbolic 5-Manifolds
Canadian journal of mathematics, Tome 55 (2003) no. 5, pp. 1080-1099

Voir la notice de l'article provenant de la source Cambridge University Press

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 $\text{vo}{{\text{l}}_{\text{5}}}\left( M \right)$ and, for $M$ compact, new estimates relating the injectivity radius and the diameter of $M$ with $\text{vo}{{\text{l}}_{\text{5}}}\left( M \right)$ . The quantification of the thin part is based upon the identification of the isometry group of the universal space by the matrix group $\text{P}{{\text{S}}_{\Delta }}\text{L}\left( 2,\,\mathbb{H} \right)$ of quaternionic $2\,\times \,2$ -matrices with Dieudonné determinant $\Delta$ equal to 1 and isolation properties of $\text{P}{{\text{S}}_{\Delta }}\text{L}\left( 2,\,\mathbb{H} \right)$ .
DOI : 10.4153/CJM-2003-042-4
Mots-clés : 53C22, 53C25, 57N16, 57S30, 51N30, 20G20, 22E40 
Kellerhals, Ruth. Quaternions and Some Global Properties of Hyperbolic 5-Manifolds. Canadian journal of mathematics, Tome 55 (2003) no. 5, pp. 1080-1099. doi: 10.4153/CJM-2003-042-4
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