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.
@article{AIF_2004__54_7_2455_0,
author = {Turaev, Vladimir},
title = {Virtual strings},
journal = {Annales de l'Institut Fourier},
volume = {54},
year = {2004},
pages = {2455-2525},
doi = {10.5802/aif.2086},
mrnumber = {2139700},
zbl = {1066.57022},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_2004__54_7_2455_0}
}
Turaev, Vladimir. Virtual strings. Annales de l'Institut Fourier, Tome 54 (2004) pp. 2455-2525. doi : 10.5802/aif.2086. http://gdmltest.u-ga.fr/item/AIF_2004__54_7_2455_0/
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