Quandle and hyperbolic volume
Ayumu Inoue
TL;DR
This paper demonstrates that the hyperbolic volume of a hyperbolic knot can be derived from quandle cocycle invariants and can determine key symmetries like invertibility and amphicheirality.
Contribution
It establishes a novel connection between hyperbolic volume and quandle cocycle invariants, enabling new insights into knot symmetries.
Findings
Hyperbolic volume is a quandle cocycle invariant.
Hyperbolic volume determines invertibility of hyperbolic knots.
Hyperbolic volume detects positive/negative amphicheirality.
Abstract
We show that the hyperbolic volume of a hyperbolic knot is a quandle cocycle invariant. Further we show that it completely determines invertibility and positive/negative amphicheirality of hyperbolic knots.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Homotopy and Cohomology in Algebraic Topology