Quandles versus symmetric quandles for oriented links

Kanako Oshiro

Quandles versus symmetric quandles for oriented links

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arxiv 2010.09983 v1 pith:DDU5S53H submitted 2020-10-20 math.GT math.AT

Kanako Oshiro This is my paper

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keywords quandlesymmetricorientedquandlesdoublegivenlinkscalled

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Given a quandle, we can construct a symmetric quandle called the symmetric double of the quandle. We show that the (co)homology groups of a given quandle are isomorphic to those of its symmetric double. Moreover, quandle coloring numbers and quandle cocycle invariants of oriented links and oriented surface-links can be interpreted by using symmetric quandles.

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Associated groups of symmetric quandles
math.GT 2025-05 accept novelty 6.0 of 10

Symmetric quandle associated groups are characterized: the underlying quandle's group is a central extension of the symmetric one with a free abelian kernel, and embeddability is equivalent.

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