We construct some cusped finite-volume hyperbolic n-manifolds Mn that fiber algebraically in all the dimensions 5 ≤ n ≤ 8. That is, there is a surjective homomorphism π 1 (Mn) → Z with finitely generated kernel.The kernel is also finitely presented in the dimensions n = 7, 8, and this leads to the first examples of hyperbolic n-manifolds Mn whose fundamental group is finitely presented but not of finite type. These n-manifolds Mn have infinitely many cusps of maximal rank and hence infinite Betti number b n−1 . They cover the finite-volume manifold Mn.We obtain these examples by assigning some appropriate colours and states to a family of right-angled hyperbolic polytopes P 5 , . . . , P 8 , and then applying some arguments of Jankiewicz -Norin -Wise [15] and . We exploit in an essential way the remarkable properties of the Gosset polytopes dual to Pn, and the algebra of integral octonions for the crucial dimensions n = 7, 8.

No abstract

We exhibit some finite-volume cusped hyperbolic 5-manifolds that fiber over the circle. These include the smallest hyperbolic 5-manifold known, discovered by Ratcliffe and Tschantz. As a consequence, we build a finite type subgroup of a hyperbolic group that is not hyperbolic.

No abstract