Some topological aspects of 4-fold symmetric quandle invariants of 3-manifolds

The paper relates the 4-fold symmetric quandle homotopy (cocycle) invariants to topological objects. We show that the 4-fold symmetric quandle homotopy invariants are at least as powerful as the DijkgraafWitten invariants. As an application, for an odd prime p, we show that the quandle cocycle invariant of a link in S ³ constructed by the Mochizuki 3-cocycle is equivalent to the DijkgraafWitten invariant with respect to /p of the double covering of S ³ branched along the link. We also reconstruct the ChernSimons invariant of closed 3-manifolds as a quandle cocycle invariant via the extended Bloch group, in analogy to [A. Inoue and Y. Kabaya, Quandle homology and complex volume, preprint(2010), arXiv:math/1012.2923].