多元亚历山大广数，VI.元胞群和 2 分量联系

arXiv - MATH - Geometric Topology Pub Date : 2024-08-21 DOI:arxiv-2408.11784

Lorenzo Traldi

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摘要

我们证明了本系列所讨论的模块和阶的两个性质：第一，基本多元亚历山大阶 $Q_A(L)$ 与链接群的元商$G(L)/G(L)''$ 中的基本阶的自然图像同构。其次，经典 2 分链路 $L$ 的中值 quandle 是由 $L$ 的还原亚历山大不变量决定的。

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Multivariate Alexander quandles, VI. Metabelian groups and 2-component links

We prove two properties of the modules and quandles discussed in this series. First, the fundamental multivariate Alexander quandle $Q_A(L)$ is isomorphic to the natural image of the fundamental quandle in the metabelian quotient $G(L)/G(L)''$ of the link group. Second, the medial quandle of a classical 2-component link $L$ is determined by the reduced Alexander invariant of $L$.

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arXiv - MATH - Geometric Topology

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