Volume 14, issue 5 (2014)

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

Volume 20
Issue 5, 2145–2685
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

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
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
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
Bibliography
1 S Asami, K Kuga, Colorings of torus knots and their twist-spuns by Alexander quandles over finite fields, J. Knot Theory Ramifications 18 (2009) 1259 MR2569560
2 K S Brown, Cohomology of groups, Graduate Texts in Mathematics 87, Springer (1982) MR1324339
3 J S Carter, D Jelsovsky, S Kamada, L Langford, M Saito, Quandle cohomology and state-sum invariants of knotted curves and surfaces, Trans. Amer. Math. Soc. 355 (2003) 3947 MR1990571
4 J S Carter, S Kamada, M Saito, Geometric interpretations of quandle homology, J. Knot Theory Ramifications 10 (2001) 345 MR1825963
5 F J B J Clauwens, The adjoint group of an Alexander quandle, arXiv:1011.1587
6 R Dijkgraaf, E Witten, Topological gauge theories and group cohomology, Comm. Math. Phys. 129 (1990) 393 MR1048699
7 M Eisermann, Quandle coverings and their Galois correspondence, to appear in Fundamenta Mathematicae
8 R Fenn, C Rourke, B Sanderson, Trunks and classifying spaces, Appl. Categ. Structures 3 (1995) 321 MR1364012
9 R Fenn, C Rourke, B Sanderson, The rack space, Trans. Amer. Math. Soc. 359 (2007) 701 MR2255194
10 A Inoue, Quandle homomorphisms of knot quandles to Alexander quandles, J. Knot Theory Ramifications 10 (2001) 813 MR1840269
11 A Inoue, Y Kabaya, Quandle homology and complex volume, (2013) arXiv:1012.2923v3
12 D Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra 23 (1982) 37 MR638121
13 Y Kabaya, Cyclic branched coverings of knots and quandle homology, Pacific J. Math. 259 (2012) 315 MR2988494
14 A Kawauchi, A survey of knot theory, Birkhäuser, Basel (1996) MR1417494
15 D Kraines, Massey higher products, Trans. Amer. Math. Soc. 124 (1966) 431 MR0202136
16 I J Leary, The mod-$\!p$ cohomology rings of some $p$–groups, Math. Proc. Cambridge Philos. Soc. 112 (1992) 63 MR1162933
17 J Mandemaker, Various topics in rack and quandle homology, Master thesis, Radboud University (2009)
18 J Milnor, On the $3$–dimensional Brieskorn manifolds $M(p,q,r)$, from: "Knots, groups, and $3$–manifolds (Papers dedicated to the memory of R H Fox)" (editor L P Neuwirth), Ann. of Math. Studies 84, Princeton Univ. Press (1975) 175 MR0418127
19 T Mochizuki, The $3$–cocycles of the Alexander quandles $\mathbb F_q[T]/(T-\omega)$, Algebr. Geom. Topol. 5 (2005) 183 MR2135551
20 T Nosaka, On quandle homology groups of Alexander quandles of prime order, Trans. Amer. Math. Soc. 365 (2013) 3413 MR3042590
21 T Nosaka, Quandle cocycles from invariant theory, Adv. Math. 245 (2013) 423 MR3084434
22 T Nosaka, Homotopical interpretation of link invariants from finite quandles, (2014) arXiv:1210.6528v5
23 M Wakui, On Dijkgraaf–Witten invariant for $3$–manifolds, Osaka J. Math. 29 (1992) 675 MR1192735