Volume 20, issue 5 (2020)

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Homology of ternary algebras yielding invariants of knots and knotted surfaces

Maciej Niebrzydowski

Algebraic & Geometric Topology 20 (2020) 2337–2372
Bibliography
1 K Ameur, M Elhamdadi, T Rose, M Saito, C Smudde, Tangle embeddings and quandle cocycle invariants, Experiment. Math. 17 (2008) 487 MR2484432
2 S Asami, S Satoh, An infinite family of non-invertible surfaces in 4–space, Bull. London Math. Soc. 37 (2005) 285 MR2119028
3 V D Belousov, nарнюе квазигруппю, Stiinca, Kishinev (1972) 227 MR0354919
4 V D Belousov, M D Sandik, N–ary quasi-groups and loops, Sibirsk. Mat. Ž. 7 (1966) 31 MR0204564
5 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
6 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
7 J S Carter, S Kamada, M Saito, Geometric interpretations of quandle homology, J. Knot Theory Ramifications 10 (2001) 345 MR1825963
8 J S Carter, M Saito, Knotted surfaces and their diagrams, 55, Amer. Math. Soc. (1998) MR1487374
9 J Certaine, The ternary operation (abc) = ab1c of a group, Bull. Amer. Math. Soc. 49 (1943) 869 MR9953
10 P M Cohn, Universal algebra, 6, Springer, Dordrecht (1981) MR620952
11 R Deviatov, Combinatorial knot invariants that detect trefoils, J. Knot Theory Ramifications 18 (2009) 1193 MR2569557
12 R Fenn, C Rourke, Racks and links in codimension two, J. Knot Theory Ramifications 1 (1992) 343 MR1194995
13 R Fenn, C Rourke, B Sanderson, James bundles, Proc. London Math. Soc. 89 (2004) 217 MR2063665
14 J Hietarinta, Labelling schemes for tetrahedron equations and dualities between them, J. Phys. A 27 (1994) 5727 MR1304207
15 J F P Hudson, Piecewise linear topology, W A Benjamin, New York (1969) MR0248844
16 D Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra 23 (1982) 37 MR638121
17 S Kamada, Knot invariants derived from quandles and racks, from: "Invariants of knots and 3–manifolds" (editors T Ohtsuki, T Kohno, T Le, J Murakami, J Roberts, V Turaev), Geom. Topol. Monogr. 4, Geom. Topol. Publ., Coventry (2002) 103 MR2002606
18 L H Kauffman, Formal knot theory, 30, Princeton Univ. Press (1983) MR712133
19 J Kim, Y Joung, S Y Lee, On generating sets of Yoshikawa moves for marked graph diagrams of surface-links, J. Knot Theory Ramifications 24 (2015) MR3346919
20 J Kim, S Nelson, Biquasile colorings of oriented surface-links, Topology Appl. 236 (2018) 64 MR3758572
21 S V Matveev, Distributive groupoids in knot theory, Mat. Sb. 119(161) (1982) 78 MR672410
22 D Needell, S Nelson, Biquasiles and dual graph diagrams, J. Knot Theory Ramifications 26 (2017) MR3666510
23 S Nelson, K Oshiro, N Oyamaguchi, Local biquandles and Niebrzydowski’s tribracket theory, Topology Appl. 258 (2019) 474 MR3933307
24 M Niebrzydowski, On some ternary operations in knot theory, Fund. Math. 225 (2014) 259 MR3205573
25 M Niebrzydowski, A Pilitowska, A Zamojska-Dzienio, Knot-theoretic ternary groups, Fund. Math. 247 (2019) 299 MR4017016
26 J H Przytycki, Fundamentals of Kauffman bracket skein modules, Kobe J. Math. 16 (1999) 45 MR1723531
27 J H Przytycki, W Rosicki, Cocycle invariants of codimension 2 embeddings of manifolds, from: "Knots in Poland III, III" (editors J H Przytycki, P Traczyk), Banach Center Publ. 103, Polish Acad. Sci. Inst. Math., Warsaw (2014) 251 MR3363816
28 D Roseman, Reidemeister-type moves for surfaces in four-dimensional space, from: "Knot theory" (editors V F R Jones, J Kania-Bartoszyńska, J H Przytycki, P Traczyk, V G Turaev), Banach Center Publ. 42, Polish Acad. Sci. Inst. Math., Warsaw (1998) 347 MR1634466
29 M Saito, S Satoh, The spun trefoil needs four broken sheets, J. Knot Theory Ramifications 14 (2005) 853 MR2187601
30 S Satoh, A Shima, The 2–twist-spun trefoil has the triple point number four, Trans. Amer. Math. Soc. 356 (2004) 1007 MR1984465
31 J D H Smith, Ternary quasigroups and the modular group, Comment. Math. Univ. Carolin. 49 (2008) 309 MR2426895
32 T G group, GAP: Groups, algorithms and programming (2018)
33 M Wada, Group invariants of links, Topology 31 (1992) 399 MR1167178
34 K Yoshikawa, An enumeration of surfaces in four-space, Osaka J. Math. 31 (1994) 497 MR1309400
35 E C Zeeman, Twisting spun knots, Trans. Amer. Math. Soc. 115 (1965) 471 MR195085