Knot quandle decomposition along a torus

Bonatto, Marco (author), Cattabriga, Alessia (author), Horvat, Eva (author)

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 the 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.

• Language: English
• Keywords: augmented fundamental quandle, links in the solid torus, satellite knots, links in lens spaces, Alexander quandle, quandle colorings
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2024
• Number of pages: 27 str.
• Numbering: Vol. 33, no. 1, art. 2350098
• PID: 20.500.12556/RUL-155462
• UDC: 51
• ISSN on article: 1793-6527
• DOI: 10.1142/S0218216523500980
• COBISS.SI-ID: 190537731
• Publication date in RUL: 03.04.2024

Record is a part of a journal

• Title: Journal of knot theory and its ramifications
• Shortened title: J. knot theory ramif.
• Publisher: World Scientific Publishing
• ISSN: 1793-6527
• COBISS.SI-ID: 520980761

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: povečani temeljni kvantil, satelitski vozli, Aleksandrov kvandel, obarvanost kvandla, matematika