Geodesic
Efficient formula of the colored Kauffman brackets
Lobachevskii journal of mathematics, Tome 16 (2004), pp. 71-78.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we introduce a formula for the homogeneous linear recursive relations of the colored Kauffman brackets, which is more effcient than the formula in $[{\rm G}_2]$.
Keywords: Colored Kauffman bracket, Kauffman bracket skein module. 
@article{LJM_2004_16_a3,
     author = {F. Nagasato},
     title = {Efficient formula of the colored {Kauffman} brackets},
     journal = {Lobachevskii journal of mathematics},
     pages = {71--78},
     publisher = {mathdoc},
     volume = {16},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2004_16_a3/}
}
TY  - JOUR
AU  - F. Nagasato
TI  - Efficient formula of the colored Kauffman brackets
JO  - Lobachevskii journal of mathematics
PY  - 2004
SP  - 71
EP  - 78
VL  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_2004_16_a3/
LA  - en
ID  - LJM_2004_16_a3
ER  - 
%0 Journal Article
%A F. Nagasato
%T Efficient formula of the colored Kauffman brackets
%J Lobachevskii journal of mathematics
%D 2004
%P 71-78
%V 16
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_2004_16_a3/
%G en
%F LJM_2004_16_a3
F. Nagasato. Efficient formula of the colored Kauffman brackets. Lobachevskii journal of mathematics, Tome 16 (2004), pp. 71-78. http://geodesic.mathdoc.fr/item/LJM_2004_16_a3/

[B] D. Bullock, “The $(2,\infty)$-skein module of the complement of a $(2,2p+1)$-torus knot”, J. Knot Theory Ramifications, 4 (1995), 619–632 | DOI | MR | Zbl

[BL] D. Bullock and W. LoFaro, The Kauffman bracket skein module of a twist knot exterior, preprint | MR

[FG] C. Frohman and R. Gelca, “Skein modules and the noncommutative torus”, Trans. Amer. Math. Soc., 352 (2000), 4877–4888 | DOI | MR | Zbl

[FGL] C. Frohman, R. Gelca and W. LoFaro, “The A-polynomial from the noncommutative viewpoint”, Trans. Amer. Math. Soc., 354 (2001), 735–747 | DOI | MR

[GL] S. Garoufalidis and T. T. Q. Le, The colored Jones function is q-holonomic, preprint | MR

[G1] R. Gelca, “Noncommutative trigonometry and the A-polynomial of the trefoil”, Math. Proc. Cambridge Phil. Soc., 133 (2002), 311–323 | DOI | MR | Zbl

[G2] R. Gelca, “On the relation between the A-polynomial and the Jones polynomial”, Proc. Amer. Math. Soc., 130 (2001), 1235–1241 | DOI | MR

[HP] J. Hoste and J. Przytycki, “The $(2,\infty)$-skein module of lens spaces; a generalization of the Jones polynomial”, J. Knot Theory Ramifications, 2 (1993), 321–333 | DOI | MR | Zbl

[L] W. B. R. Lickorish, “The skein method for three-manifold invariants”, J. Knot Theory Ramifications, 2 (1993), 171–194 | DOI | MR | Zbl

[N] F. Nagasato, “Computing the A-polynomial using noncommutative methods”, J. Knot Theory Ramifications, 14:6 (2005), 735–749 | DOI | MR | Zbl

[P1] J. Przytycki, “Skein modules of 3-manifolds”, Bull. Pol. Acad. Sci., 39 (1991), 91–100 | MR

[P2] J. Przytycki, “Fundamentals of Kauffman bracket skein module”, Kobe J. Math., 16:1 (1999), 45–66 | MR | Zbl

[S] N. Saveliev, Lectures on the topology of 3-manifolds: an introduction to the Casson invariant, de Gruyter textbook, Walter de Gruyter, Berlin, 1999 | MR | Zbl