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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