Knot quandle decomposition along a torus

Fuente: arXiv
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Hauptverfasser: Bonatto, Marco, Cattabriga, Alessia, Horvat, Eva
Format: Preprint
Veröffentlicht: 2020
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author Bonatto, Marco
Cattabriga, Alessia
Horvat, Eva
author_facet Bonatto, Marco
Cattabriga, Alessia
Horvat, Eva
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2009_12869
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Knot quandle decomposition along a torus
Bonatto, Marco
Cattabriga, Alessia
Horvat, Eva
Geometric Topology
57K10, 57K12, 57K14
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.
title Knot quandle decomposition along a torus
topic Geometric Topology
57K10, 57K12, 57K14
url https://arxiv.org/abs/2009.12869