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Knot quandle decomposition along a torus.
- 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 :
- *TORUS
*KNOT theory
Subjects
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