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

Volume 26
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

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
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
Skew-rack cocycle invariants of closed $3$-manifolds

Takefumi Nosaka

Algebraic & Geometric Topology 26 (2026) 1451–1464
DOI: 10.2140/agt.2026.26.1451
Bibliography
1 M Aschenbrenner, S Friedl, H Wilton, 3-manifold groups, European Mathematical Society (2015) MR3444187
2 V G Bardakov, T R Nasybullov, M V Neshchadim, Twisted conjugacy classes of the unit element, Sibirsk. Mat. Zh. 54 (2013) 20 MR3089322
3 J S Carter, M Elhamdadi, M Graña, M Saito, Cocycle knot invariants from quandle modules and generalized quandle homology, Osaka J. Math. 42 (2005) 499 MR2166720
4 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
5 J Ceniceros, M Elhamdadi, M Green, S Nelson, Augmented biracks and their homology, Internat. J. Math. 25 (2014) 1450087 MR3266530
6 R Dijkgraaf, E Witten, Topological gauge theories and group cohomology, Comm. Math. Phys. 129 (1990) 393 MR1048699
7 R Fenn, C Rourke, On Kirby’s calculus of links, Topology 18 (1979) 1 MR528232
8 R Fenn, C Rourke, B Sanderson, An introduction to species and the rack space, from: "Topics in knot theory" (editor M E Bozhüyük), NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 399, Kluwer (1993) 33 MR1257904
9 R Fenn, C Rourke, B Sanderson, Trunks and classifying spaces, Appl. Categ. Structures 3 (1995) 321 MR1364012
10 D L Gonçalves, T Nasybullov, On groups where the twisted conjugacy class of the unit element is a subgroup, Comm. Algebra 47 (2019) 930 MR3938527
11 M Hedden, M H Kim, T E Mark, K Park, Irreducible 3-manifolds that cannot be obtained by 0-surgery on a knot, Trans. Amer. Math. Soc. 372 (2019) 7619 MR4029676
12 S Kamada, Quandles with good involutions, their homologies and knot invariants, from: "Intelligence of low dimensional topology 2006" (editors J S Carter, S Kamada, L H Kauffman, A Kawauchi, T Kohno), Ser. Knots Everything 40, World Sci. (2007) 101 MR2371714
13 S Kamada, K Oshiro, Homology groups of symmetric quandles and cocycle invariants of links and surface-links, Trans. Amer. Math. Soc. 362 (2010) 5501 MR2657689
14 R Kirby, A calculus for framed links in S3, Invent. Math. 45 (1978) 35 MR467753
15 T Nosaka, Quandles and topological pairs : symmetry, knots, and cohomology, Springer (2017) MR3729413
16 N Reshetikhin, V G Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991) 547 MR1091619
17 V G Turaev, Quantum invariants of knots and 3-manifolds, 18, De Gruyter (2016) MR3617439