Virtual strings  [ Cordes virtuelles ]
Annales de l'Institut Fourier, Tome 54 (2004) no. 7, p. 2455-2525
Une corde virtuelle est un schéma d'auto-intersections d'une courbe fermée sur une surface. Nous étudions les invariants algébriques des cordes virtuelles ainsi que deux relations d'équivalence sur l'ensemble des cordes : homotopie et cobordisme. Nous montrons que les invariants d'homotopie de cordes forment un groupe de Lie de dimension infinie. Les rapports avec les noeuds virtuels sont également abordés.
A virtual string is a scheme of self-intersections of a closed curve on a surface. We study algebraic invariants of strings as well as two equivalence relations on the set of strings: homotopy and cobordism. We show that the homotopy invariants of strings form an infinite dimensional Lie group. We also discuss connections between virtual strings and virtual knots.
DOI : https://doi.org/10.5802/aif.2086
Classification:  57M99
Mots clés: cordes virtuelles, noeuds virtuels, surfaces, cobordisme, matrices antisymétriques, co-crochet de Lie
@article{AIF_2004__54_7_2455_0,
     author = {Turaev, Vladimir},
     title = {Virtual strings},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {7},
     year = {2004},
     pages = {2455-2525},
     doi = {10.5802/aif.2086},
     zbl = {1066.57022},
     mrnumber = {2139700},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2004__54_7_2455_0}
}
Turaev, Vladimir. Virtual strings. Annales de l'Institut Fourier, Tome 54 (2004) no. 7, pp. 2455-2525. doi : 10.5802/aif.2086. http://www.numdam.org/item/AIF_2004__54_7_2455_0/

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