Volume 5, issue 2 (2005)

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

Volume 25
Issue 7, 3789–4436
Issue 6, 3145–3787
Issue 5, 2527–3144
Issue 4, 1917–2526
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

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
Yang–Baxter deformations of quandles and racks

Michael Eisermann

Algebraic & Geometric Topology 5 (2005) 537–562
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