论文标题
某些双曲线4个manifolds的代数振动
Algebraic fibrations of certain hyperbolic 4-manifolds
论文作者
论文摘要
代数纤维组是对较高维度的纤维3型脉络膜组的代数概括。令$ m（\ Mathcal {p}）$和$ m（\ Mathcal {e}）$为与多双曲右角的24-Cell $ \ Mathcal $ \ Mathcal {p} $相关的强度和紧凑的双曲线真实的瞬间角歧管，并且是超轻的右手右右手右右手$ \ Mathcal $ \ Mathcal} $} jankiewicz-norin wise在[13]中表明，$π_1（m（\ mathcal {p}）））$和$π_1（m（\ mathcal {e}））$是代数纤维。也就是说，有两个确切的序列$$ 1 \ rightArrow h _ {\ Mathcal {p}} \rightArolowπ_1（m（\ Mathcal {p}））\ xrightArrow {\ xrightArrow {\ x _ { h _ {\ Mathcal {e}} \rightarrowπ_1（m（\ Mathcal {e}）））\ xrightArrow {ϕ _ {\ m nathcal {\ Mathcal {e}}}}}}} \ Mathbb {z} $ h _ {\ Mathcal {e}} $有限生成。在本文中，我们进一步表明$ h _ {\ Mathcal {p}} $和$ h _ {\ Mathcal {e}} $不是$ fp_2 $。特别是，这些纤维内核组是有限生成的，但没有有限的呈现。
Algebraically fibering group is an algebraic generalization of the fibered 3-manifold group in higher dimensions. Let $M(\mathcal{P})$ and $M(\mathcal{E})$ be the cusped and compact hyperbolic real moment-angled manifolds associated to the hyperbolic right-angled 24-cell $\mathcal{P}$ and the hyperbolic right-angled 120-cell $\mathcal{E}$, respectively. Jankiewicz-Norin-Wise showed in [13] that $π_1(M(\mathcal{P}))$ and $π_1(M(\mathcal{E}))$ are algebraic fibered. Namely, there are two exact sequences $$1\rightarrow H_{\mathcal{P}}\rightarrow π_1(M(\mathcal{P}))\xrightarrow{ϕ_{\mathcal{P}}} \mathbb{Z}\rightarrow 1,$$ $$1\rightarrow H_{\mathcal{E}}\rightarrow π_1(M(\mathcal{E}))\xrightarrow{ϕ_{\mathcal{E}}} \mathbb{Z}\rightarrow 1,$$ where $H_{\mathcal{P}}$ and $H_{\mathcal{E}}$ are finitely generated. In this paper, we furtherly show that the groups $H_{\mathcal{P}}$ and $H_{\mathcal{E}}$ are not $FP_2$. In particular, those fiber-kernel groups are finitely generated, but not finitely presented.
