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

By Takefumi Nosaka

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 $\Z$-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.Comment: The results in this paper will be generalized in another pape

Topics: Mathematics - Geometric Topology, Mathematics - Algebraic Geometry, Mathematics - Algebraic Topology, Mathematics - Group Theory
Year: 2012
DOI identifier: 10.2140/agt.2014.14.2655
OAI identifier: oai:arXiv.org:1103.3839
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