Classifying links and spatial graphs with finite $N$-quandles

Fuente: arXiv
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Main Author: Mellor, Blake
Format: Preprint
Published: 2023
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_version_ 1866917294185119744
author Mellor, Blake
author_facet Mellor, Blake
contents The fundamental quandle is a complete invariant for unoriented tame knots \cite{JO, Ma} and non-split links \cite{FR}. The proof involves proving a relationship between the components of the fundamental quandle and the cosets of the peripheral subgroup(s) in the fundamental group of the knot or link. We extend these relationships to spatial graphs, and to $N$-quandles of links and spatial graphs. As an application, we are able to give a complete list of links with finite $N$-quandles, proving a conjecture from \cite{MS}, and a partial list of spatial graphs with finite $N$-quandles.
format Preprint
id arxiv_https___arxiv_org_abs_2304_05537
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Classifying links and spatial graphs with finite $N$-quandles
Mellor, Blake
Geometric Topology
57K12, 57M15
The fundamental quandle is a complete invariant for unoriented tame knots \cite{JO, Ma} and non-split links \cite{FR}. The proof involves proving a relationship between the components of the fundamental quandle and the cosets of the peripheral subgroup(s) in the fundamental group of the knot or link. We extend these relationships to spatial graphs, and to $N$-quandles of links and spatial graphs. As an application, we are able to give a complete list of links with finite $N$-quandles, proving a conjecture from \cite{MS}, and a partial list of spatial graphs with finite $N$-quandles.
title Classifying links and spatial graphs with finite $N$-quandles
topic Geometric Topology
57K12, 57M15
url https://arxiv.org/abs/2304.05537