TY - JOUR
T1 - On third homologies of groups and of quandles via the Dijkgraaf–Witten invariant and Inoue–Kabaya map
AU - Nosaka, Takefumi
N1 - Publisher Copyright:
© 2014 Mathematical Sciences Publishers. All Rights reserved.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 2014/11/6
Y1 - 2014/11/6
N2 - 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.
AB - 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.
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U2 - 10.2140/agt.2014.14.2655
DO - 10.2140/agt.2014.14.2655
M3 - Article
AN - SCOPUS:84910616034
VL - 14
SP - 2655
EP - 2691
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
SN - 1472-2747
IS - 5
ER -