Algebraic fibrations of certain hyperbolic 4-manifolds
Algebraic fibrations of certain hyperbolic 4-manifolds
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某些双曲 4-流形的代数纤维化
DOI：
10.1016/j.topol.2021.107592
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发表时间：
2020-01
影响因子：
0.6
通讯作者：
Jiming Ma
中科院分区：
文献类型：
--
作者：
Fangting Zheng;Jiming Ma
代数纤维群是纤维 3 流形群在更高维度的代数推广。令 M (P) 和 M (E) 分别为与双曲直角 24 单元 P 和双曲直角 120 单元 E 相关的尖点紧双曲实矩角流形。 Jankiewicz、Norin 和 Wise 最近证明 π 1 (M (P)) 和 π 1 (M (E)) 是代数纤维化的。换句话说，存在两个精确序列 1→ H P→ π 1 (M (P))→ phi P Z→ 1, 1→ H E→ π 1 (M (E))→ phi E Z→ 1，其中 HP 和 H E 是有限生成的。在本文中，我们进一步证明纤维核群 H P 和 H E 不是 F P 2 。特别是，它们是有限生成的，但不是有限呈现的。
An algebraically fibering group is an algebraic generalization of the fibered 3-manifold group in higher dimensions. Let M (P) and M (E) be the cusped and compact hyperbolic real moment-angled manifolds associated with the hyperbolic right-angled 24-cell P and the hyperbolic right-angled 120-cell E, respectively. Jankiewicz, Norin, and Wise recently showed that π 1 (M (P)) and π 1 (M (E)) are algebraically fibered. In other words, there are two exact sequences 1→ H P→ π 1 (M (P))→ ϕ P Z→ 1, 1→ H E→ π 1 (M (E))→ ϕ E Z→ 1, where H P and H E are finitely generated. In this paper, we further show that the fiber-kernel groups H P and H E are not F P 2. In particular, they are finitely generated, but not finitely presented.