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Knot quandle decomposition along a torus
ID Bonatto, Marco (Author), ID Cattabriga, Alessia (Author), ID Horvat, Eva (Author)

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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 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 This link opens in a new window
UDC:51
ISSN on article:1793-6527
DOI:10.1142/S0218216523500980 This link opens in a new window
COBISS.SI-ID:190537731 This link opens in a new window
Publication date in RUL:03.04.2024
Views:218
Downloads:33
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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 This link opens in a new window

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

Projects

Funder:Other - Other funder or multiple funders
Funding programme:INdAM, National Group for Algebraic and Geometric Structures, and their Applications (GNSAGA)

Funder:Other - Other funder or multiple funders
Funding programme:University of Bologna

Funder:ARRS - Slovenian Research Agency
Project number:P1-0292
Name:Topologija in njena uporaba

Funder:ARRS - Slovenian Research Agency
Project number:N1-0083
Name:Forsing, fuzija in kombinatorika odprtih pokritij

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