LAUSR

Abstract 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, we introduce row relation maps with respect to Alexander pairs, and we 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, we can obtain a shadow quandle 2-cocycle and additionally a shadow quandle cocycle invariant. We also discuss the fact that a generalized quandle cocycle invariant is a shadow quandle cocycle invariant.