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The length of a 3-cocycle of the 5-dihedral quandle. (English) Zbl 1356.57021
The main result of the paper states that the length of the Mochizuki 3-cocycle of the 5-dihedral quandle is eight. Consequently, the 2-twist-spun figure-eight knot and the 2-twist-spun (2,5)-torus knot have the triple point number eight. The result is achieved through detailed investigation of all 3-cocycles of length at most seven.
MSC:
57Q45 Knots and links in high dimensions (PL-topology) (MSC2010)
18G99 Homological algebra in category theory, derived categories and functors
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