Geodesic
Khovanov homology of graph-links
Sbornik. Mathematics, Tome 203 (2012) no. 8, pp. 1196-1210 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Graph-links arise as the intersection graphs of turning chord diagrams of links. Speaking informally, graph-links provide a combinatorial description of links up to mutations. Many link invariants can be reformulated in the language of graph-links. Khovanov homology, a well-known and useful knot invariant, is defined for graph-links in this paper (in the case of the ground field of characteristic two). Bibliography: 14 titles.
Keywords: graph-links, Khovanov homology. 
@article{SM_2012_203_8_a5,
     author = {I. M. Nikonov},
     title = {Khovanov homology of graph-links},
     journal = {Sbornik. Mathematics},
     pages = {1196--1210},
     year = {2012},
     volume = {203},
     number = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2012_203_8_a5/}
}
TY  - JOUR
AU  - I. M. Nikonov
TI  - Khovanov homology of graph-links
JO  - Sbornik. Mathematics
PY  - 2012
SP  - 1196
EP  - 1210
VL  - 203
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/SM_2012_203_8_a5/
LA  - en
ID  - SM_2012_203_8_a5
ER  - 
%0 Journal Article
%A I. M. Nikonov
%T Khovanov homology of graph-links
%J Sbornik. Mathematics
%D 2012
%P 1196-1210
%V 203
%N 8
%U http://geodesic.mathdoc.fr/item/SM_2012_203_8_a5/
%G en
%F SM_2012_203_8_a5
I. M. Nikonov. Khovanov homology of graph-links. Sbornik. Mathematics, Tome 203 (2012) no. 8, pp. 1196-1210. http://geodesic.mathdoc.fr/item/SM_2012_203_8_a5/

[1] D. P. Ilyutko, V. O. Manturov, “Introduction to graph-link theory”, J. Knot Theory Ramifications, 18:6 (2009), 791–823 | DOI | MR | Zbl

[2] D. P. Il'yutko, V. O. Manturov, “Graph-links”, Dokl. Math., 80:2 (2009), 739–742 | DOI | MR | Zbl

[3] D. Ilyutko, V. Manturov, “Graph-links”, Introductory lectures on knot theory (Trieste, 2009), Ser. Knots Everything, 46, World Scientific, Hackensack, NJ, 2012, 135–161 | MR | Zbl

[4] L. Ghier, “Double occurrence words with the same alternance graph”, Ars Combin., 36 (1993), 57–64 | MR | Zbl

[5] S. V. Chmutov, S. K. Lando, “Mutant knots and intersection graphs”, Algebr. Geom. Topol., 7 (2007), 1579–1598 | DOI | MR | Zbl

[6] L. Traldi, L. Zulli, “A bracket polynomial for graphs. I”, J. Knot Theory Ramifications, 18:12 (2009), 1681–1709 | DOI | MR | Zbl

[7] L. Traldi, “A bracket polynomial for graphs. II. Links, Euler circuits and marked graphs”, J. Knot Theory Ramifications, 19:4 (2010), 547–586 | DOI | MR | Zbl

[8] D. P. Ilyutko, An equivalence between the set of graph-knots and the set of homotopy classes of looped graphs, arXiv: 0911.5504

[9] D. P. Il'yutko, “Framed 4-graphs: Euler tours, Gauss circuits and rotating circuits”, Sb. Math., 202:9 (2011), 1303–1326 | DOI | MR | Zbl

[10] M. Khovanov, “A categorification of the Jones polynomial”, Duke Math. J., 101:3 (1997), 359–426 | DOI | MR | Zbl

[11] P. Ozsvath, J. Rasmussen, Z. Szabó, Odd Khovanov homology, arXiv: 0710.4300

[12] J. M. Bloom, “Odd Khovanov homology is mutation invariant”, Math. Res. Lett., 17:1 (2010), 1–10 | MR | Zbl

[13] S. M. Wehrli, Khovanov Homology and Conway Mutation, arXiv: 0301312

[14] A. Bouchet, “Circle graph obstructions”, J. Combin. Theory Ser. B, 60:1 (1994), 107–144 | DOI | MR | Zbl