Casson invariant of knots associated with divides
Algebra i analiz, Tome 15 (2003) no. 4, pp. 236-252.

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A formula for the Casson invariant of knots associated with divides is presented. The formula is written in terms of Arnold's invariants of pieces of the divide. Various corollaries are discussed.
Keywords: divide, Casson invariant, Arnold's invariants of plane curves.
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A. Shumakovich. Casson invariant of knots associated with divides. Algebra i analiz, Tome 15 (2003) no. 4, pp. 236-252. http://geodesic.mathdoc.fr/item/AA_2003_15_4_a8/

[1] A'Campo N., “Le groupe de monodromie du déploiement des singularites isolées de courbes planes. II”, Proceedings of the International Congress of Mathematicians, Vol. 1 (Vancouver, BC, 1974), Canad. Math. Congress, Montreal, Que., 1975, 395–404 | MR

[2] A'Campo N., “Real deformations and complex topology of plane curve singularities”, Ann. Fac. Sci. Toulouse Math. (6), 8 (1999), 5–23 ; arXiv:alg-geom/9710023 | MR

[3] A'Campo N., “Generic immersions of curves, knots, monodromy and Gordian number”, Inst. Hautes Études Sci. Publ. Math., 88 (1998), 1999, 151–169 ; arXiv: math.GT/9803081 | MR

[4] A'Campo N., “Planar trees, slalom curves and hyperbolic knots”, Inst. Hautes Études Sci. Publ. Math., 88 (1998), 1999, 171–180 ; arXiv:math.GT/9906087 | MR

[5] Aicardi F., “Tree-like curves, Singularities and Bifurcations”, Adv. Soviet Math., 21 (1994), 1–31, Amer. Math. Soc., Providence, RI | MR

[6] Arnol'd V. I., “Plane curves, their invariants, perestroikas and classifications”, Singularities and Bifurcations, Adv. Soviet Math., 21, Amer. Math. Soc., Providence, RI, 1994, 33–91 | MR | Zbl

[7] Chmutov S., An integral generalization of the Gusein–Zade–Natanzon theorem, arXiv:math.GT/0207238 | MR

[8] Chmutov S., Duzhin S., “Explicit formulas for Arnold's generic curve invariants”, The Arnold–Gelfand Mathematical Seminars, Birkhäuser Boston, Boston, MA, 1997, 123–138 | MR | Zbl

[9] Gibson W., Ishikawa M., “Links of oriented divides and fibrations in link exteriors”, Osaka J. Math., 39:3 (2002), 681–703 | MR | Zbl

[10] Hirasawa M., “Visualization of A'Campo's fibered links and unknotting operation”, Proceedings of the First Joint Japan–Mexico Meeting in Topology (Morelia, 1999), Topology Appl., 121, no. 1–2, 2002, 287–304 | MR | Zbl

[11] Polyak M., “Invariants of curves and fronts via Gauss diagrams”, Topology, 37:5 (1998), 989–1009 | DOI | MR | Zbl

[12] Shumakovich A., “Yavnye formuly dlya strannosti ploskoi krivoi”, Algebra i analiz, 7:3 (1995), 165–199 | MR | Zbl

[13] Viro O. Ya., First degree invariants of generic curves on surfaces, Preprint no. 21, Dep. Math. Uppsala Univ., Uppsala, 1994