Algebraic fibrations of certain hyperbolic 4-manifolds

Jiming Ma; Fangting Zheng

doi:10.1016/j.topol.2021.107592

Algebraic fibrations of certain hyperbolic 4-manifolds

Jiming Ma, Fangting Zheng^*

^*Corresponding author for this work

Department of Pure Mathematics

Fudan University

Research output: Contribution to journal › Article › peer-review

Abstract

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 π₁(M(P)) and π₁(M(E)) are algebraically fibered. In other words, there are two exact sequences 1→H_P→π₁(M(P))→ϕ_PZ→1, 1→H_E→π₁(M(E))→ϕ_EZ→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 FP₂. In particular, they are finitely generated, but not finitely presented.

Original language	English
Article number	107592
Journal	Topology and its Applications
Volume	290
DOIs	https://doi.org/10.1016/j.topol.2021.107592
Publication status	Published - 1 Mar 2021

Keywords

Algebraic fibered
Finitely generated
Finitely presented
Hyperbolic 4-manifolds

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10.1016/j.topol.2021.107592

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title = "Algebraic fibrations of certain hyperbolic 4-manifolds",

abstract = "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 π1(M(P)) and π1(M(E)) are algebraically fibered. In other words, there are two exact sequences 1→HP→π1(M(P))→ϕPZ→1, 1→HE→π1(M(E))→ϕEZ→1, where HP and HE are finitely generated. In this paper, we further show that the fiber-kernel groups HP and HE are not FP2. In particular, they are finitely generated, but not finitely presented.",

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AU - Zheng, Fangting

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N2 - 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 π1(M(P)) and π1(M(E)) are algebraically fibered. In other words, there are two exact sequences 1→HP→π1(M(P))→ϕPZ→1, 1→HE→π1(M(E))→ϕEZ→1, where HP and HE are finitely generated. In this paper, we further show that the fiber-kernel groups HP and HE are not FP2. In particular, they are finitely generated, but not finitely presented.

AB - 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 π1(M(P)) and π1(M(E)) are algebraically fibered. In other words, there are two exact sequences 1→HP→π1(M(P))→ϕPZ→1, 1→HE→π1(M(E))→ϕEZ→1, where HP and HE are finitely generated. In this paper, we further show that the fiber-kernel groups HP and HE are not FP2. In particular, they are finitely generated, but not finitely presented.

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Algebraic fibrations of certain hyperbolic 4-manifolds

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Keywords

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