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Skein module deformations of elementary moves on links

Jozef H Przytycki

Geometry & Topology Monographs 4 (2002) 313–335

DOI: 10.2140/gtm.2002.4.313

Bibliography
1 R P Anstee, J H Przytycki, D Rolfsen, Knot polynomials and generalized mutation, Topology Appl. 32 (1989) 237–249 MR1007103
2 N A Askitas, A note on 4–equivalence, J. Knot Theory Ramifications 8 (1999) 261–263 MR1691441
3 F Bonahon, L Siebenmann, Geometric splittings of classical knots and the algebraic knots of Conway, from: "New geometric splittings of classical knots" (editor L Siebenmann), London Math. Soc. Lecture Notes Ser. 75 (2003)
4 R H Bruck, A survey of binary systems, Ergebnisse der Mathematik und ihrer Grenzgebiete 20, Springer Verlag (1958) MR0093552
5 Q Chen, The 3–move conjecture for 5–braids, from: "Knots in Hellas '98 (Delphi)", Ser. Knots Everything 24, World Sci. Publ., River Edge, NJ (2000) 36–47 MR1865699
6 J H Conway, An enumeration of knots and links, and some of their algebraic properties, from: "Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967)", Pergamon (1970) 329–358 MR0258014
7 H S M Coxeter, Factor groups of the braid group, from: "Proc. Fourth Canadian Math. Congress, Banff" (1957) 95–122
8 M K Dąbkowski, J H Przytycki, Burnside obstructions to the Montesinos–Nakanishi 3–move conjecture, Geom. Topol. 6 (2002) 355–360 MR1914572
9 M K Dąbkowski, J H Przytycki, Burnside groups and rational moves, in preparation
10 J Dymara, T Januszkiewicz, J H Przytycki, Symplectic structure on colorings, Lagrangian tangles and Tits buildings, preprint (2001)
11 R Fenn, C Rourke, Racks and links in codimension two, J. Knot Theory Ramifications 1 (1992) 343–406 MR1194995
12 J Hoste, J H Przytycki, A survey of skein modules of 3–manifolds, from: "Knots 90 (Osaka, 1990)", de Gruyter (1992) 363–379 MR1177433
13 A Mednykh, J H Przytycki, An interview with W Thurston, Warsaw, August 1983 A Mednykh could not come to the International Congress of Mathematicians in Warsaw (August 1983) so he sent me a list of questions to W Thurston. I met with Thurston and asked him the questions to which he kindly replied in length. Then I wrote his answers (sometimes with my comments).
14 F Jaeger, J H Przytycki, A non-commutative version of the Goeritz matrix of a link, in preparation
15 V F R Jones, On a certain value of the Kauffman polynomial, Comm. Math. Phys. 125 (1989) 459–467 MR1022523
16 D Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra 23 (1982) 37–65 MR638121
17 R Kirby, Problems in low-dimensional topology, from: "Geometric topology (Athens, GA, 1993)", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 35–473 MR1470751 Edited by Rob Kirby
18 W B R Lickorish, The unknotting number of a classical knot, from: "Combinatorial methods in topology and algebraic geometry (Rochester, N.Y., 1982)", Contemp. Math. 44, Amer. Math. Soc. (1985) 117–121 MR813107
19 A Mednykh, A Vesnin, Covering properties of small volume hyperbolic 3–manifolds, J. Knot Theory Ramifications 7 (1998) 381–392 MR1625364
20 J M Montesinos, Lectures on 3–fold simple coverings and 3–manifolds, from: "Combinatorial methods in topology and algebraic geometry (Rochester, N.Y., 1982)", Contemp. Math. 44, Amer. Math. Soc. (1985) 157–177 MR813111
21 H Murakami, Some metrics on classical knots, Math. Ann. 270 (1985) 35–45 MR769605
22 Y Nakanishi, Fox's congruence modulo (2,1), Sūrikaisekikenkyūsho Kōkyūroku 813 (1984) 102–110
23 Y Nakanishi, S Suzuki, On Fox's congruence classes of knots, Osaka J. Math. 24 (1987) 217–225 MR881755
24 J H Przytycki, tk moves on links, from: "Braids (Santa Cruz, CA, 1986)", Contemp. Math. 78, Amer. Math. Soc. (1988) 615–656 MR975099
25 J H Przytycki, 3–coloring and other elementary invariants of knots, from: "Knot theory (Warsaw, 1995)", Banach Center Publ. 42, Polish Acad. Sci. (1998) 275–295 MR1634462
26 J H Przytycki, Skein modules of 3–manifolds, Bull. Polish Acad. Sci. Math. 39 (1991) 91–100 MR1194712
27 J H Przytycki, Search for different links with the same Jones' type polynomials: ideas from graph theory and statistical mechanics, from: "Panoramas of mathematics (Warsaw, 1992/1994)", Banach Center Publ. 34, Polish Acad. Sci. (1995) 121–148 MR1374344
28 J H Przytycki, Three talks in Cuautitlan under the general title: Topologia algebraica basada sobre nudos, from: "Proceedings of the First International Workshop on “Graphs – Operads – Logic”, Cuautitlan, Mexico, March 12-16, 2001" (2004) arXiv:math.GT/0109029
29 J H Przytycki, P Traczyk, M Veve, notes from the March 2000 workshop at the Banach Center, Warsaw (2000)
30 J H Przytycki, T Tsukamoto, The fourth skein module and the Montesinos–Nakanishi conjecture for 3–algebraic links, J. Knot Theory Ramifications 10 (2001) 959–982 MR1867103
31 D Rolfsen, Knots and links, Mathematics Lecture Series 7, Publish or Perish (1976) MR0515288
32 Y W Rong, The Kauffman polynomial and the two-fold cover of a link, Indiana Univ. Math. J. 40 (1991) 321–331 MR1101234
33 A Stoimenow, Polynomial values, the linking form and unknotting numbers, Math. Res. Lett. 11 (2004) 755–769 MR2106240
34 P Traczyk, A criterion for signed unknotting number, from: "Low-dimensional topology (Funchal, 1998)", Contemp. Math. 233, Amer. Math. Soc. (1999) 215–220 MR1701685
35 T Tsukamoto, The fourth skein module for 4–algebraic links, PhD thesis, George Washington University (2000)
36 V G Turaev, The Conway and Kauffman modules of a solid torus, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 167 (1988) 79–89, 190 MR964255
37 M Vaughan-Lee, The restricted Burnside problem, London Mathematical Society Monographs. New Series 8, The Clarendon Press Oxford University Press (1993) MR1364414
38 O Viro, personal communication at Gdansk topology conference (Jankowski memorial) May 24–25 2002; also email to the author October 18 2002
39 M Wada, Group invariants of links, Topology 31 (1992) 399–406 MR1167178
40 H Wendt, Die gordische Auflösung von Knoten, Math. Z. 42 (1937) 680–696 MR1545700