[Nœuds non-mutants avec le même polynôme de Jones colorié]
On construit des familles (finies) de taille quelconque de nœuds hyperboliques non-mutants avec le même polynôme de Jones colorié.
We construct arbitrarily large (finite) families of hyperbolic non-mutant knots with equal colored Jones polynomial.
Accepté le :
Publié le :
@article{CRMATH_2009__347_13-14_809_0,
author = {Stoimenow, Alexander},
title = {Non-mutants with equal colored {Jones} polynomial},
journal = {Comptes Rendus. Math\'ematique},
pages = {809--811},
publisher = {Elsevier},
volume = {347},
number = {13-14},
year = {2009},
doi = {10.1016/j.crma.2009.03.029},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.03.029/}
}
TY - JOUR AU - Stoimenow, Alexander 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 UR - http://www.numdam.org/articles/10.1016/j.crma.2009.03.029/ DO - 10.1016/j.crma.2009.03.029 LA - en ID - CRMATH_2009__347_13-14_809_0 ER -
%0 Journal Article %A Stoimenow, Alexander %T Non-mutants with equal colored Jones polynomial %J Comptes Rendus. Mathématique %D 2009 %P 809-811 %V 347 %N 13-14 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.03.029/ %R 10.1016/j.crma.2009.03.029 %G en %F CRMATH_2009__347_13-14_809_0
Stoimenow, Alexander. Non-mutants with equal colored Jones polynomial. Comptes Rendus. Mathématique, Tome 347 (2009) no. 13-14, pp. 809-811. doi : 10.1016/j.crma.2009.03.029. http://www.numdam.org/articles/10.1016/j.crma.2009.03.029/
[1] On enumeration of knots and links (Leech, J., ed.), Computational Problems in Abstract Algebra, Pergamon Press, 1969, pp. 329-358
[2] Distinguishing mutants by knot polynomials, J. Knot Theory Ramifications, Volume 5 (1996) no. 2, pp. 225-238
[3] 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] A new polynomial invariant of knots and links, Bull. Amer. Math. Soc., Volume 12 (1985), pp. 239-246
[5] KnotScape, a knot polynomial calculation and table access program http://www.math.utk.edu/~morwen (available at)
[6] A polynomial invariant of knots and links via von Neumann algebras, Bull. Amer. Math. Soc., Volume 12 (1985), pp. 103-111
[7] 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] Polynomials of 2-cable-like links, Proc. Amer. Math. Soc., Volume 100 (1987), pp. 355-361
[10] A polynomial invariant for oriented links, Topology, Volume 26 (1987) no. 1, pp. 107-141
[11] 3-valent graphs and the Kauffman bracket, Pacific J. Math., Volume 164 (1994), pp. 361-381
[12] The Jones polynomial of satellite links around mutants (Birman, J.S.; Libgober, A., 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] Mutation and volumes of knots in , Invent. Math., Volume 90 (1987) no. 1, pp. 189-215
[15] Hard to identify (non-)mutations, Math. Proc. Cambridge Philos. Soc., Volume 141 (2006) no. 2, pp. 281-285
[16] On cabled knots and Vassiliev invariants (not) contained in knot polynomials, Canad. J. Math., Volume 59 (2007) no. 2, pp. 418-448
[17] Mutation and the colored Jones polynomial, with an appendix by Daniel Matei (preprint) | arXiv
Cité par Sources :
