Quandle cocycle invariants of links using Mochizuki's 3-cocycles and Dijkgraaf-Witten invariants of 3-manifolds

Abstract

T. Mochizuki determined all 3-cocycles of the third quandle cohomologies of Alexander quandles on finite fields. We show that all the 3-cocycles, except those of 2-cocycle forms, are derived from group 3-cocycles of a meta-abelian group. Further, the quandle cocycle invariant of a link using Mochizuki's 3-cocycle is equivalent to a $\mathbb{Z}$-equivariant part of the Dijkgraaf-Witten invariant of a cyclic covering of $S^3$ branched over the link using the group. We compute some Massey triple products via the former invariant.

The results in this paper will be generalized in another paper

References in corpus (2)

• The mod-p cohomology rings of some p-groups
• The 3-cocycles of the Alexander quandles F_q[T]/(T-omega)

Cited by in corpus (1)

• Heap and Ternary Self-Distributive Cohomology