Volume 14, issue 5 (2014)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
On third homologies of groups and of quandles via the Dijkgraaf–Witten invariant and Inoue–Kabaya map

Takefumi Nosaka

Algebraic & Geometric Topology 14 (2014) 2655–2692
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 –equivariant parts of the Dijkgraaf–Witten invariants of some cyclic branched covering spaces, via some cocycle invariant of links.

Keywords
quandle, group homology, $3$–manifolds, link, branched covering, Massey product
Mathematical Subject Classification 2010
Primary: 20J06, 57M12
Secondary: 57M27, 57N65
References
Publication
Received: 9 February 2013
Revised: 8 October 2013
Accepted: 14 October 2013
Published: 5 November 2014
Authors
Takefumi Nosaka
Faculty of Mathematics
Kyushu University
744, Motooka, Nishi-ku
Fukuoka 819-0395
Japan