扭曲亚历山大多项式和矩阵加权zeta函数

IF 0.6 4区数学 Q3 MATHEMATICS Kyushu Journal of Mathematics Pub Date : 2020-01-01 DOI:10.2206/kyushujm.74.211

H. Goda

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引用次数: 0

摘要

。扭曲亚历山大多项式是结对及其群表示的不变量。本文引入了由有向结图得到的有向图，用于研究结的扭曲亚历山大多项式。在这种情况下，我们证明了一个结的扭曲Alexander多项式的逆可以看作是矩阵加权的zeta函数，它是有向加权图的Ihara-Selberg zeta函数的推广。

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 POLYNOMIAL AND MATRIX-WEIGHTED ZETA FUNCTION

. The twisted Alexander polynomial is an invariant of the pair of a knot and its group representation. Herein, we introduce a digraph obtained from an oriented knot diagram, which is used to study the twisted Alexander polynomial of knots. In this context, we show that the inverse of the twisted Alexander polynomial of a knot may be regarded as the matrix-weighted zeta function that is a generalization of the Ihara–Selberg zeta function of a directed weighted graph.

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来源期刊

Kyushu Journal of Mathematics 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total. More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.