SOME TOPOLOGICAL ASPECTS OF 4-FOLD SYMMETRIC QUANDLE INVARIANTS OF 3-MANIFOLDS

作者：Hatakenaka Eri^*; Nosaka Takefumi

来源：International Journal of Mathematics, 2012, 23(7): 1250064.

DOI：10.1142/S0129167X12500644

• Quandle
• link
• 3-manifold
• branched covering
• Dijkgraaf-Witten invariant
• Chern-Simons invariant

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 Dijkgraaf-Witten 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 Dijkgraaf-Witten invariant with respect to Z/pZ of the double covering of S-3 branched along the link. We also reconstruct the Chern-Simons 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].

• 出版日期2012-7