We establish a quandle version of the twisted Alexander polynomial. We also develop a theory that reduces the size of a twisted Alexander matrix with column relations. The reduced matrix can be used to refine invariants derived from the twisted Alexander matrix.
The first author was supported by JSPS KAKENHI Grant Number 18K03292. The second author was supported by JSPS KAKENHI Grant Number 21K03233.
"Quandle twisted Alexander invariants." Osaka J. Math. 59 (3) 683 - 702, July 2022.