Comptes Rendus
no. 13-14
Topology
Non-mutants with equal colored Jones polynomial
Presented by: Étienne Ghys
Alexander Stoimenow1
1BK21 Project, Department of Mathematical Sciences, KAIST, Daejeon 307-701, Republic of Korea
Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 809-811

We construct arbitrarily large (finite) families of hyperbolic non-mutant knots with equal colored Jones polynomial.

On construit des familles (finies) de taille quelconque de nœuds hyperboliques non-mutants avec le même polynôme de Jones colorié.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.03.029

Alexander Stoimenow  1

1 BK21 Project, Department of Mathematical Sciences, KAIST, Daejeon 307-701, Republic of Korea 
@article{CRMATH_2009__347_13-14_809_0,
     author = {Alexander Stoimenow},
     title = {Non-mutants with equal colored {Jones} polynomial},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {809--811},
     year = {2009},
     publisher = {Elsevier},
     volume = {347},
     number = {13-14},
     doi = {10.1016/j.crma.2009.03.029},
     language = {en},
}
TY  - JOUR
AU  - Alexander Stoimenow
TI  - Non-mutants with equal colored Jones polynomial
JO  - Comptes Rendus. Mathématique
PY  - 2009
SP  - 809
EP  - 811
VL  - 347
IS  - 13-14
PB  - Elsevier
DO  - 10.1016/j.crma.2009.03.029
LA  - en
ID  - CRMATH_2009__347_13-14_809_0
ER  - 
%0 Journal Article
%A Alexander Stoimenow
%T Non-mutants with equal colored Jones polynomial
%J Comptes Rendus. Mathématique
%D 2009
%P 809-811
%V 347
%N 13-14
%I Elsevier
%R 10.1016/j.crma.2009.03.029
%G en
%F CRMATH_2009__347_13-14_809_0
Alexander Stoimenow. Non-mutants with equal colored Jones polynomial. Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 809-811. doi: 10.1016/j.crma.2009.03.029

[1] J.H. Conway On enumeration of knots and links (J. Leech, ed.), Computational Problems in Abstract Algebra, Pergamon Press, 1969, pp. 329-358

[2] P.R. Cromwell; H.R. Morton Distinguishing mutants by knot polynomials, J. Knot Theory Ramifications, Volume 5 (1996) no. 2, pp. 225-238

[3] D. De Wit; J. Links Where the Links–Gould invariant first fails to distinguish nonmutant prime knots, J. Knot Theory Ramifications, Volume 16 (2007) no. 8, pp. 1021-1041 | arXiv

[4] P. Freyd; J. Hoste; W.B.R. Lickorish; K. Millett; A. Ocneanu; D. Yetter A new polynomial invariant of knots and links, Bull. Amer. Math. Soc., Volume 12 (1985), pp. 239-246

[5] J. Hoste; M. Thistlethwaite KnotScape, a knot polynomial calculation and table access program http://www.math.utk.edu/~morwen (available at)

[6] V.F.R. Jones A polynomial invariant of knots and links via von Neumann algebras, Bull. Amer. Math. Soc., Volume 12 (1985), pp. 103-111

[7] L.H. Kauffman An invariant of regular isotopy, Trans. Amer. Math. Soc., Volume 318 (1990), pp. 417-471

[8] R. Kirby (Ed.), Problems of Low-Dimensional Topology, book available on http://math.berkeley.edu/~kirby

[9] W.B.R. Lickorish; A.S. Lipson Polynomials of 2-cable-like links, Proc. Amer. Math. Soc., Volume 100 (1987), pp. 355-361

[10] W.B.R. Lickorish; K.C. Millett A polynomial invariant for oriented links, Topology, Volume 26 (1987) no. 1, pp. 107-141

[11] G. Masbaum; P. Vogel 3-valent graphs and the Kauffman bracket, Pacific J. Math., Volume 164 (1994), pp. 361-381

[12] H.R. Morton; P. Traczyk The Jones polynomial of satellite links around mutants (J.S. Birman; A. Libgober, eds.), Braids, Contemporary Mathematics, vol. 78, Amer. Math. Soc., 1988, pp. 587-592

[13] J. Murakami, Finite type invariants detecting the mutant knots, in “Knot theory”, the Murasugi 70th birthday schrift, 1999, pp. 258–267

[14] D. Ruberman Mutation and volumes of knots in S3, Invent. Math., Volume 90 (1987) no. 1, pp. 189-215

[15] A. Stoimenow Hard to identify (non-)mutations, Math. Proc. Cambridge Philos. Soc., Volume 141 (2006) no. 2, pp. 281-285

[16] A. Stoimenow On cabled knots and Vassiliev invariants (not) contained in knot polynomials, Canad. J. Math., Volume 59 (2007) no. 2, pp. 418-448

[17] A. Stoimenow; T. Tanaka Mutation and the colored Jones polynomial, with an appendix by Daniel Matei (preprint) | arXiv

Cited by Sources:

Comments - Policy