Knot quandle decomposition along a torus
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.
Keywords
povečani temeljni kvantil;satelitski vozli;Aleksandrov kvandel;obarvanost kvandla;
Data
| Language: | English |
|---|---|
| Year of publishing: | 2024 |
| Typology: | 1.01 - Original Scientific Article |
| Organization: | UL PEF - Faculty of Education |
| UDC: | 51 |
| COBISS: |
190537731
|
| ISSN: | 1793-6527 |
| Views: | 34 |
| Downloads: | 7 |
| Average score: | 0 (0 votes) |
| Metadata: |
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Other data
| Secondary language: | Slovenian |
|---|---|
| Secondary keywords: | Matematika; |
| Type (COBISS): | Article |
| Pages: | 27 str. (PDF) |
| Volume: | ǂissue ǂ1 |
| Issue: | ǂart. ǂ2350098 |
| Chronology: | 2024 |
| DOI: | 10.1142/S0218216523500980 |
| ID: | 23332604 |
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