The length of a 3–cocycle of the 5–dihedral quandle

Satoh, Shin

doi:10.2140/agt.2016.16.3325

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The length of a $3$–cocycle of the $5$–dihedral quandle

Shin Satoh

Algebraic & Geometric Topology 16 (2016) 3325–3359

DOI: 10.2140/agt.2016.16.3325

Abstract

We determine the length of the Mochizuki $3$ –cocycle of the $5$ –dihedral quandle. This induces that the $2$ –twist-spun figure-eight knot and the $2$ –twist-spun $(2, 5)$ –torus knot have the triple point number eight.

Dedicated to Professor Taizo Kanenobu on the occasion of his 60th birthday

Keywords

surface-knot, triple point number, quandle, cocycle invariant, coloring

Mathematical Subject Classification 2010

Primary: 57Q45

Secondary: 57Q35

References

Publication

Received: 1 August 2015

Revised: 5 October 2015

Accepted: 20 October 2015

Published: 15 December 2016

Authors

Shin Satoh
Department of Mathematics Kobe University Rokkodai-cho 1-1 Nada-ku Kobe 657 8501 Japan

Volume 16, issue 6 (2016)