Algebraic & Geometric Topology Volume 23, issue 4 (2023)

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Bialgebraic approach to rack cohomology

Simon Covez, Marco Andrés Farinati, Victoria Lebed and Dominique Manchon

Algebraic & Geometric Topology 23 (2023) 1551–1582

DOI: 10.2140/agt.2023.23.1551

Bibliography

1	N Andruskiewitsch, M Graña, From racks to pointed Hopf algebras, Adv. Math. 178 (2003) 177 MR1994219
2	J S Carter, M Elhamdadi, M Saito, Homology theory for the set-theoretic Yang–Baxter equation and knot invariants from generalizations of quandles, Fund. Math. 184 (2004) 31 MR2128041
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	S Carter, S Kamada, M Saito, Surfaces in 4–space, 142, Springer (2004) MR2060067
5	F Clauwens, The algebra of rack and quandle cohomology, J. Knot Theory Ramifications 20 (2011) 1487 MR2854230
6	S Covez, On the conjectural Leibniz cohomology for groups, J. K–Theory 10 (2012) 519 MR3019457
7	S Covez, Rack homology and conjectural Leibniz homology, preprint (2014) arXiv:1402.1625
8	P Dehornoy, Braids and self-distributivity, 192, Birkhäuser (2000) MR1778150
9	M Elhamdadi, S Nelson, Quandles—an introduction to the algebra of knots, 74, Amer. Math. Soc. (2015) MR3379534
10	M A Farinati, J García Galofre, A differential bialgebra associated to a set theoretical solution of the Yang–Baxter equation, J. Pure Appl. Algebra 220 (2016) 3454 MR3497972
11	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
12	R Fenn, C Rourke, B Sanderson, Trunks and classifying spaces, Appl. Categ. Structures 3 (1995) 321 MR1364012
13	R Fenn, C Rourke, B Sanderson, The rack space, Trans. Amer. Math. Soc. 359 (2007) 701 MR2255194
14	D Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra 23 (1982) 37 MR638121
15	M K Kinyon, Leibniz algebras, Lie racks, and digroups, J. Lie Theory 17 (2007) 99 MR2286884
16	V Lebed, Homologies of algebraic structures via braidings and quantum shuffles, J. Algebra 391 (2013) 152 MR3081627
17	V Lebed, Cohomology of idempotent braidings with applications to factorizable monoids, Internat. J. Algebra Comput. 27 (2017) 421 MR3668103
18	R A Litherland, S Nelson, The Betti numbers of some finite racks, J. Pure Appl. Algebra 178 (2003) 187 MR1952425
19	S V Matveev, Distributive groupoids in knot theory, Mat. Sb. 119(161) (1982) 78 MR672410
20	J H Przytycki, Distributivity versus associativity in the homology theory of algebraic structures, Demonstratio Math. 44 (2011) 823 MR2906433
21	J H Przytycki, Knots and distributive homology : from arc colorings to Yang–Baxter homology, from: "New ideas in low dimensional topology" (editors L H Kauffman, V O Manturov), Ser. Knots Everything 56, World Sci. (2015) 413 MR3381331
22	J H Przytycki, K K Putyra, Homology of distributive lattices, J. Homotopy Relat. Struct. 8 (2013) 35 MR3031593
23	J H Przytycki, K K Putyra, The degenerate distributive complex is degenerate, Eur. J. Math. 2 (2016) 993 MR3572555
24	J H Przytycki, W Rosicki, Cocycle invariants of codimension 2 embeddings of manifolds, from: "Knots in Poland, III" (editors J H Przytycki, P Traczyk), Banach Center Publ. 103, Polish Acad. Sci. Inst. Math. (2014) 251 MR3363816
25	M Ronco, Primitive elements in a free dendriform algebra, from: "New trends in Hopf algebra theory" (editors N Andruskiewitsch, W R Ferrer Santos, H J Schneider), Contemp. Math. 267, Amer. Math. Soc. (2000) 245 MR1800716
26	M Rosso, Groupes quantiques et algèbres de battage quantiques, C. R. Acad. Sci. Paris Sér. I Math. 320 (1995) 145 MR1320345
27	J P Serre, Homologie singulière des espaces fibrés : applications, Ann. of Math. 54 (1951) 425 MR45386
28	M Szymik, Permutations, power operations, and the center of the category of racks, Comm. Algebra 46 (2018) 230 MR3764859
29	M Takasaki, Abstraction of symmetric transformations, Tôhoku Math. J. 49 (1943) 145 MR21002