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

Takefumi Nosaka

    Research output: Contribution to journalArticlepeer-review

    6 Citations (Scopus)

    Abstract

    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
    Volume14
    Issue number5
    DOIs
    Publication statusPublished - Nov 6 2014

    All Science Journal Classification (ASJC) codes

    • Geometry and Topology

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