The second quandle homology of the Takasaki quandle of an odd abelian group is an exterior square of the group

Details The second quandle homology of the Takasaki quandle of an odd abelian group is an exterior square of the group The second quandle homology of the Takasaki quandle of an odd abelian group is an exterior square of the group

2010-06-01

arxiv.org/abs/1006.0258v1

Mathematics

Geometric Topology

6 pages, 1 figure

Scientific paper

We prove that if G is an abelian group of odd order then there is an
isomorphism from the second quandle homology of the Takasaki quandle of G to
the exterior square of G. In particular, for G=Z_k^n, k odd, we obtain
Z_k^{n(n-1)/2}. Nontrivial second homology allows us to use 2-cocycles to
construct new quandles from T(G), and to construct link invariants.

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