Geodesic
A Jones polynomial for braid-like isotopies of oriented links and its categorification
Audoux, Benjamin1 ; Fiedler, Thomas1
1Laboratoire E.Picard, Université Paul Sabatier, Toulouse, France
Algebraic and Geometric Topology, Tome 5 (2005) no. 4, pp. 1535-1553
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

A braid-like isotopy for links in 3–space is an isotopy which uses only those Reidemeister moves which occur in isotopies of braids. We define a refined Jones polynomial and its corresponding Khovanov homology which are, in general, only invariant under braid-like isotopies.

DOI : 10.2140/agt.2005.5.1535
Keywords: braid-like isotopies, Jones polynomials, Khovanov homologies

Audoux, Benjamin  1   ; Fiedler, Thomas  1

1 Laboratoire E.Picard, Université Paul Sabatier, Toulouse, France 
@article{10_2140_agt_2005_5_1535,
     author = {Audoux, Benjamin and Fiedler, Thomas},
     title = {A {Jones} polynomial for braid-like isotopies of oriented links and its categorification},
     journal = {Algebraic and Geometric Topology},
     pages = {1535--1553},
     year = {2005},
     volume = {5},
     number = {4},
     doi = {10.2140/agt.2005.5.1535},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.1535/}
}
TY  - JOUR
AU  - Audoux, Benjamin
AU  - Fiedler, Thomas
TI  - A Jones polynomial for braid-like isotopies of oriented links and its categorification
JO  - Algebraic and Geometric Topology
PY  - 2005
SP  - 1535
EP  - 1553
VL  - 5
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.1535/
DO  - 10.2140/agt.2005.5.1535
ID  - 10_2140_agt_2005_5_1535
ER  - 
%0 Journal Article
%A Audoux, Benjamin
%A Fiedler, Thomas
%T A Jones polynomial for braid-like isotopies of oriented links and its categorification
%J Algebraic and Geometric Topology
%D 2005
%P 1535-1553
%V 5
%N 4
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.1535/
%R 10.2140/agt.2005.5.1535
%F 10_2140_agt_2005_5_1535
Audoux, Benjamin; Fiedler, Thomas. A Jones polynomial for braid-like isotopies of oriented links and its categorification. Algebraic and Geometric Topology, Tome 5 (2005) no. 4, pp. 1535-1553. doi: 10.2140/agt.2005.5.1535

[1] M M Asaeda, J H Przytycki, A S Sikora, Categorification of the Kauffman bracket skein module of $I$–bundles over surfaces, Algebr. Geom. Topol. 4 (2004) 1177

[2] B Audoux, Homologie de Khovanov, preprint (2005)

[3] J S Birman, Braids, links, and mapping class groups, Annals of Mathematics Studies 82, Princeton University Press (1974)

[4] G Burde, H Zieschang, Knots, de Gruyter Studies in Mathematics 5, Walter de Gruyter Co. (1985)

[5] T Fiedler, A small state sum for knots, Topology 32 (1993) 281

[6] T Fiedler, Gauss diagram invariants for knots and links, Mathematics and its Applications 532, Kluwer Academic Publishers (2001)

[7] J Hoste, J H Przytycki, An invariant of dichromatic links, Proc. Amer. Math. Soc. 105 (1989) 1003

[8] L H Kauffman, State models and the Jones polynomial, Topology 26 (1987) 395

[9] M Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359

[10] H R Morton, Infinitely many fibred knots having the same Alexander polynomial, Topology 17 (1978) 101

[11] O Viro, Remarks on definition of Khovanov homology

Cité par Sources :