Virtual strings
[Cordes virtuelles]
Annales de l'Institut Fourier, Tome 54 (2004) no. 7, pp. 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 : 10.5802/aif.2086
Classification : 57M99
Keywords: Virtual strings, virtual knots, surfaces, cobordism, skew-symmetric matrices, Lie cobracket
Mot clés : cordes virtuelles, noeuds virtuels, surfaces, cobordisme, matrices antisymétriques, co-crochet de Lie
Turaev, Vladimir 1

1 Université Louis Pasteur, IRMA, CNRS, 7 rue René Descartes, 67084 Strasbourg (France)
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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/articles/10.5802/aif.2086/

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