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Fundamental 2-quandles of the M(1/2, 1/3, 1/3; k) Montesino Knots

2024
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Thesis / Dissertation Description

Every oriented knot has an associated fundamental quandle. Except in two simple cases, these quandles have infinite order. For every integer n>1, there is a quotient of the fundamental quandle called the n-quandle of the knot. In some cases, these n-quandles may be finite. In the case of the M(1/2,1/3,1/3; k) Montesino knot family, the 2-quandle is finite. In this paper, we investigate the structure of the 2-quandle and prove its size.

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