We construct some cusped finite-volume hyperbolic n-manifolds $M^n$ that fibre algebraically in all the dimensions $5\leq n \leq 8$. That is, there is a surjective homomorphism $\pi _1(M^n) \to {\mathbb {Z}}$ 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 $\widetilde M^n$ whose fundamental group is finitely presented but not of finite type. These n-manifolds $\widetilde M^n$ have infinitely many cusps of maximal rank and, hence, infinite Betti number $b_{n-1}$. They cover the finite-volume manifold $M^n$. We obtain these examples by assigning some appropriate colours and states to a family of right-angled hyperbolic polytopes $P^5, \ldots , P^8$, and then applying some arguments of Jankiewicz, Norin and Wise [18] and Bestvina and Brady [7]. We exploit in an essential way the remarkable properties of the Gosset polytopes dual to $P^n$, and the algebra of integral octonions for the crucial dimensions $n=7,8$.

我们构造了一些尖点有限体积双曲n流形$M^n$，它们在所有维度$5\leq n \leq 8$上以代数方式纤维化。也就是说，存在有限生成核的满射同态$\pi _1(M^n) \to {\mathbb {Z}}$。核也在维度$n=7, 8$中有限地呈现，这导致了双曲n流形$\widetilde M^n$的第一个例子，其基本群是有限地呈现的，但不是有限类型的。这些n流形$\widetilde M^n$具有无限多个最大等级的尖点，因此，贝蒂数$b_{n-1}$是无限的。它们涵盖有限体积流形$M^n$。我们通过将一些适当的颜色和状态分配给一系列直角双曲多胞形$P^5, \ldots , P^8$来获得这些示例，然后应用 Jankiewicz、Norin 和 Wise [18] 以及 Bestvina 和布雷迪[7]。我们以一种重要的方式利用了对偶$P^n$的戈塞特多胞体的显着性质，以及关键维度$n=7,8$的整数八元数的代数。