TY - JOUR

T1 - On sufficiency of the definition of MCQ Alexander pairs in terms of invariants for handlebody-knots

AU - Murao, Tomo

N1 - Funding Information:
The author would like to thank Atsushi Ishii for his helpful comments. This work was supported by JSPS KAKENHI Grant Numbers JP20K22312 and JP21K13796.
Publisher Copyright:
© 2022, The Managing Editors.

PY - 2022

Y1 - 2022

N2 - A multiple conjugation quandle is an algebraic structure whose axioms are motivated from handlebody-knot theory. By using an MCQ Alexander pair f, which is a pair of maps corresponding to a linear extension of a multiple conjugation quandle, we can construct the f-twisted Alexander matrices, which produce invariants for handlebody-knots. The purpose of this paper is to show the sufficiency of the definition of MCQ Alexander pairs in constructing the f-twisted Alexander matrices from the aspect of linear extensions of multiple conjugation quandles. Furthermore, we introduce the notion of cohomologous for MCQ Alexander pairs, which induces the same invariant for handlebody-knots.

AB - A multiple conjugation quandle is an algebraic structure whose axioms are motivated from handlebody-knot theory. By using an MCQ Alexander pair f, which is a pair of maps corresponding to a linear extension of a multiple conjugation quandle, we can construct the f-twisted Alexander matrices, which produce invariants for handlebody-knots. The purpose of this paper is to show the sufficiency of the definition of MCQ Alexander pairs in constructing the f-twisted Alexander matrices from the aspect of linear extensions of multiple conjugation quandles. Furthermore, we introduce the notion of cohomologous for MCQ Alexander pairs, which induces the same invariant for handlebody-knots.

KW - Cohomologous

KW - f-twisted Alexander matrix

KW - Handlebody-knot

KW - MCQ Alexander pair

KW - Multiple conjugation quandle

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U2 - 10.1007/s13366-022-00652-0

DO - 10.1007/s13366-022-00652-0

M3 - Article

AN - SCOPUS:85133692432

SN - 0138-4821

JO - Beitrage zur Algebra und Geometrie

JF - Beitrage zur Algebra und Geometrie

ER -