Row relations of twisted Alexander matrices and shadow quandle 2-cocycles
type: Item
instance of: scholarly article
title: Row relations of twisted Alexander matrices and shadow quandle 2-cocycles
zbMATH Open document ID: 1480.57005
author: Atsushi Ishii
author: Kanako Oshiro
published in: Topology and its Applications
publication date: 2021-09-27T00:00:00Z
review text: The authors continue their study of Alexander pairs \((f_1,f_2)\) and \((f_1 , f_2 )\)-twisted 2-cocycles, see [\textit{A. Ishii} and \textit{K. Oshiro}, ``Twisted derivatives with Alexander pairs for quandles'', Preprint]. An Alexander pair \((f_1 , f_2 )\) and an \((f_1 , f_2 )\)-twisted 2-cocycle can be used to define a generalization of twisted Alexander matrices and twisted Alexander invariants. In this paper, the authors introduce row relation maps with respect to Alexander pairs, and show the following two properties: First, a row relation map gives a linear relation among the row vectors of an \((f_1 , f_2 )\)-twisted Alexander matrix. Second, given an \((f_1 , f_2 )\)-twisted 2-cocycle and a row relation map, the authors obtain a shadow quandle 2-cocycle and additionally a shadow quandle cocycle invariant. The authors also discuss the fact that a generalized quandle cocycle invariant is a shadow quandle cocycle invariant.
reviewed by: Claus Ernst
Mathematics Subject Classification ID: 57K10
Mathematics Subject Classification ID: 57K12
zbMATH DE Number: 7401499
zbMATH Keywords: row relations
zbMATH Keywords: Alexander matrices
zbMATH Keywords: quandles
zbMATH Keywords: shadow quandle 2-cocycles
zbMATH Keywords: generalized quandle 2-cocycles
zbMATH Keywords: shadow quandle cocycle invariants
MaRDI profile type: Publication
full work available at URL: j.topol.2020.107513
OpenAlex ID: W3112477285
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DOI: 10.1016/J.TOPOL.2020.107513
description: scientific article; zbMATH DE number 7401499