Geodesic
Invariants of homotopy classes of curves and graphs on $2$-surfaces
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 4, pp. 89-105 
V. O. Manturov; D. A. Fedoseev. Invariants of homotopy classes of curves and graphs on $2$-surfaces. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 4, pp. 89-105. http://geodesic.mathdoc.fr/item/FPM_2013_18_4_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Algebraic objects arising from the study of curves and graphs on $2$-surfaces are studied. Their homotopy invariance is verified.

[1] Ilyutko D. P., Manturov V. O., Nikonov I. M., “Chëtnost v teorii uzlov i graf-zatsepleniya”, SMFN, 41, 2011, 3–163 | MR

[2] Manturov V. O., “Kompleks Khovanova dlya virtualnykh uzlov”, Fundament. i prikl. mat., 11:4 (2005), 127–152 | MR | Zbl

[3] Fomenko A. T., “The theory of invariants of multidimensional integrable Hamiltonian systems (with arbitrary many degrees of freedom). Molecular table of all integrable systems with two degrees of freedom”, Amer. Math. Soc., 6 (1991), 1–35 | MR | Zbl

[4] Goldman W., “Invariant functions on Lie groups and Hamiltonian flows of surface group representations”, Invent. Math., 85 (1986), 263–302 | DOI | MR | Zbl

[5] Hass J., Scott P., “Shortening curves on surfaces”, Topology, 33:1 (1994), 25–43 | DOI | MR | Zbl

[6] Reinhart B. L., “Algorithms for Jordan curves on compact surfaces”, Ann. Math., 75:2 (1962), 209–222 | DOI | MR | Zbl

[7] Turaev V. G., “Skein quantization of Poisson algebras of loops on surfaces”, Ann. Sci. École Norm. Sup., 24 (1991), 635–704 | MR | Zbl