论文标题
纤维纤维纤维上的双曲线歧管，直至尺寸8
Hyperbolic manifolds that fiber algebraically up to dimension 8
论文作者
论文摘要
我们在所有尺寸中构建了一些有限的有限体积$ n $ n $ n $ -manifolds $ m_n $，$ 5 \ leq n \ leq 8 $。也就是说，有一个有限生成的内核的汇总同态$π_1（m_n）\ to \ mathbb z $。 内核也有限地显示在尺寸$ n = 7，8 $中，这导致了双曲线$ n $ -n $ manifolds $ \ widetilde m_n $的第一个示例，其基本组的基本组有限地呈现但不是有限类型。这些$ n $ -manifolds $ \ widetilde m_n $具有无限的最大排名，因此无限的betti number $ b_ {n-1} $。它们涵盖了有限体积歧管$ m_n $。 我们通过将一些适当的颜色和状态分配给一个右角双曲线多型$ P_5，\ ldots，p_8 $，然后应用Jankiewicz，Norin，Wise，Wise和Bestvina，Brady的一些参数。我们以必不可少的方式利用了戈塞特多型偶性至$ p_n $的显着属性，以及关键维度的积分八元代数$ n = 7,8 $。
We construct some cusped finite-volume hyperbolic $n$-manifolds $M_n$ that fiber algebraically in all the dimensions $5\leq n \leq 8$. That is, there is a surjective homomorphism $π_1(M_n) \to \mathbb Z$ 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, Wise and Bestvina, Brady. 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 $n=7,8$.
