Virtual strings
Annales de l'Institut Fourier, Volume 54 (2004) no. 7, p. 2455-2525
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.
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.
DOI : https://doi.org/10.5802/aif.2086
Classification:  57M99
Keywords: Virtual strings, virtual knots, surfaces, cobordism, skew-symmetric matrices, Lie cobracket
@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, Volume 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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