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2018•arXiv (Cornell University)Open access

On the knot quandle of a fibered knot, finiteness and equivalence of knot quandles

Ayumu Inoue

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Abstract

We show that the structure of a fibered knot, as a fiber bundle, is reflected in its knot quandle. As an application, we discuss finiteness and equivalence of knot quandles of concrete fibered 2-knots.

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What this paper is about

We show that the structure of a fibered knot, as a fiber bundle, is reflected in its knot quandle. As an application, we discuss finiteness and equivalence of knot quandles of concrete fibered 2-knots.

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Available abstract

We show that the structure of a fibered knot, as a fiber bundle, is reflected in its knot quandle. As an application, we discuss finiteness and equivalence of knot quandles of concrete fibered 2-knots.

Key concepts: Fibered knot, Knot (papermaking), Mathematics, Pure mathematics, Tricolorability, Knot invariant, Equivalence (formal languages), Knot theory

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