On third homologies of groups and of quandles via the Dijkgraaf–Witten invariant and Inoue–Kabaya map

Takefumi Nosaka

Research output: Contribution to journalArticle

3 Citations (Scopus)


We propose a simple method for producing quandle cocycles from group cocycles by a modification of the Inoue–Kabaya chain map. Further, we show that, with respect to “universal extension of quandles”, the chain map induces an isomorphism between third homologies (modulo some torsion). For example, all Mochizuki’s quandle 3–cocycles are shown to be derived from group cocycles. As an application, we calculate some Z–equivariant parts of the Dijkgraaf–Witten invariants of some cyclic branched covering spaces, via some cocycle invariant of links.

Original languageEnglish
Pages (from-to)2655-2691
Number of pages37
JournalAlgebraic and Geometric Topology
Issue number5
Publication statusPublished - Nov 6 2014


All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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