Algebraic & Geometric Topology Volume 5, issue 2 (2005)

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Yang–Baxter deformations of quandles and racks

Michael Eisermann

Algebraic & Geometric Topology 5 (2005) 537–562

DOI: 10.2140/agt.2005.5.537

Bibliography

1	E Artin, Theory of braids, Ann. of Math. $(2)$ 48 (1947) 101 MR0019087
2	R J Baxter, Partition function of the eight-vertex lattice model, Ann. Physics 70 (1972) 193 MR0290733
3	R J Baxter, Exactly solved models in statistical mechanics, Academic Press [Harcourt Brace Jovanovich Publishers] (1982) MR690578
4	J S Birman, Braids, links, and mapping class groups, Annals of Mathematics Studies 82, Princeton University Press (1974) MR0375281
5	E Brieskorn, Automorphic sets and braids and singularities, from: "Braids (Santa Cruz, CA, 1986)", Contemp. Math. 78, Amer. Math. Soc. (1988) 45 MR975077
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	V G Drinfel’d, Quantum groups, from: "Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986)", Amer. Math. Soc. (1987) 798 MR934283
8	V G Drinfel’d, On some unsolved problems in quantum group theory, from: "Quantum groups (Leningrad, 1990)", Lecture Notes in Math. 1510, Springer (1992) 1 MR1183474
9	M Eisermann, Homological characterization of the unknot, J. Pure Appl. Algebra 177 (2003) 131 MR1954330
10	M Eisermann, Knot colouring polynomials, Pacific J. Math. 231 (2007) 305 MR2346499
11	P Etingof, M Graña, On rack cohomology, J. Pure Appl. Algebra 177 (2003) 49 MR1948837
12	P Etingof, T Schedler, A Soloviev, Set-theoretical solutions to the quantum Yang–Baxter equation, Duke Math. J. 100 (1999) 169 MR1722951
13	L Faddeev, Integrable models in $(1+1)$–dimensional quantum field theory, from: "Recent advances in field theory and statistical mechanics (Les Houches, 1982)", North-Holland (1984) 561 MR782509
14	R Fenn, C Rourke, Racks and links in codimension two, J. Knot Theory Ramifications 1 (1992) 343 MR1194995
15	R Fenn, C Rourke, B Sanderson, The rack space, Trans. Amer. Math. Soc. 359 (2007) 701 MR2255194
16	P J Freyd, D N Yetter, Braided compact closed categories with applications to low-dimensional topology, Adv. Math. 77 (1989) 156 MR1020583
17	M Gerstenhaber, On the deformation of rings and algebras, Ann. of Math. $(2)$ 79 (1964) 59 MR0171807
18	M Gerstenhaber, S D Schack, Algebras, bialgebras, quantum groups, and algebraic deformations, from: "Deformation theory and quantum groups with applications to mathematical physics (Amherst, MA, 1990)", Contemp. Math. 134, Amer. Math. Soc. (1992) 51 MR1187279
19	V F R Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. $($N.S.$)$ 12 (1985) 103 MR766964
20	V F R Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. $(2)$ 126 (1987) 335 MR908150
21	V F R Jones, On knot invariants related to some statistical mechanical models, Pacific J. Math. 137 (1989) 311 MR990215
22	D Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra 23 (1982) 37 MR638121
23	C Kassel, Quantum groups, Graduate Texts in Mathematics 155, Springer (1995) MR1321145
24	C Kassel, M Rosso, V Turaev, Quantum groups and knot invariants, Panoramas et Synthèses 5, Société Mathématique de France (1997) MR1470954
25	L H Kauffman, Knots and physics, Series on Knots and Everything 1, World Scientific Publishing Co. (2001) MR1858113
26	J H Lu, M Yan, Y C Zhu, On the set-theoretical Yang–Baxter equation, Duke Math. J. 104 (2000) 1 MR1769723
27	S V Matveev, Distributive groupoids in knot theory, Mat. Sb. $($N.S.$)$ 119(161) (1982) 78, 160 MR672410
28	V G Turaev, The Yang–Baxter equation and invariants of links, Invent. Math. 92 (1988) 527 MR939474
29	C N Yang, Some exact results for the many-body problem in one dimension with repulsive delta-function interaction, Phys. Rev. Lett. 19 (1967) 1312 MR0261870
30	D N Yetter, Topological quantum field theories associated to finite groups and crossed $G$–sets, J. Knot Theory Ramifications 1 (1992) 1 MR1155090
31	D N Yetter, Functorial knot theory, Series on Knots and Everything 26, World Scientific Publishing Co. (2001) MR1834675