结群表示的扭曲亚历山大不变量

arXiv: Geometric Topology Pub Date : 2020-02-24 DOI:10.3836/tjm/1502179346

Takefumi Nosaka

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引用次数: 1

摘要

给定一个结群到固定群的同态，引入一个K_1 -群的元，它是(扭曲)Alexander多项式的推广。我们将这个K_1类与其他的亚历山大多项式进行比较。对于半局部环，我们计算了一些结点的K_1 -类，并证明了它们的非平凡性。我们也引入亚元亚历山大多项式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Twisted Alexander Invariants of Knot Group Representations

Given a homomorphism from a knot group to a fixed group, we introduce an element of a $K_1$-group, which is a generalization of (twisted) Alexander polynomials. We compare this $K_1$-class with other Alexander polynomials. In terms of semi-local rings, we compute the $K_1$-classes of some knots and show their non-triviality. We also introduce metabelian Alexander polynomials.

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arXiv: Geometric Topology

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