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Knot quandle decomposition along a torus.

Authors :
Bonatto, Marco
Cattabriga, Alessia
Horvat, Eva
Source :
Journal of Knot Theory & Its Ramifications. Jan2024, Vol. 33 Issue 1, p1-27. 27p.
Publication Year :
2024

Abstract

We study the structure of the augmented fundamental quandle of a knot whose complement contains an incompressible torus. We obtain the relationship between the fundamental quandle of a satellite knot and the fundamental quandles/groups of its companion and pattern knots. General presentations of the fundamental quandles of a link in a solid torus, a link in a lens space and a satellite knot are described. In the last part of this paper, an algebraic approach to the study of affine quandles is presented and some known results about the Alexander module and quandle colorings are obtained. [ABSTRACT FROM AUTHOR]

Subjects

Subjects :
*TORUS
*KNOT theory

Details

Language :
English
ISSN :
02182165
Volume :
33
Issue :
1
Database :
Academic Search Index
Journal :
Journal of Knot Theory & Its Ramifications
Publication Type :
Academic Journal
Accession number :
176194833
Full Text :
https://doi.org/10.1142/S0218216523500980