Geodesic
Cocycle invariants for links in the projective space
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 12 (2010), pp. 88-97 Cet article a éte moissonné depuis la source Math-Net.Ru

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We introduce a definition of proper colorings of the diagram by the elements of the finite groupoid. We introduce an invariant for links in the projective space, based on the cocycle homology theory.
Keywords: link, projective space
Mots-clés : groupoid, quandle, cocycle invariant. 
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D. V. Gorkovets. Cocycle invariants for links in the projective space. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 12 (2010), pp. 88-97. http://geodesic.mathdoc.fr/item/VCHGU_2010_12_a10/

[1] N. Andruskiewitsch, M. Graña, “From racks to pointed Hopf algebras”, Adv. in Math., 178:2 (2003), 177–243

[2] Scott Carter, A Survey of Quandle Ideas, 2010, arXiv: 1002.4429 [math.GT]

[3] Scott Carter, Mohamed Elhamdadi, Marias Graña, Masahico Saito, “Generalizations of Quandle Cocycles Invariants and Alexander Modules from Quandle Modules”, Osaka J. Math., 42 (2005), 499–541

[4] Scott Carter, Mohamed Elhamdadi, Masahico Saito, “Twisted quandle homology theory and cocycle knot invariants”, Algebraic Geometric Topology, 2 (2002), 95–135

[5] Scott Carter, Seiishi Kamada, Daniel Jelsovsky, Laurel Langford, Masahico Saito, “Quandle Cohomology and State-sum Invariants of Knotted Curves and Surfaces”, Trans. Amer. Math. Soc., 355 (2003), 3947–3989

[6] D. Joyce, “A classifying invariant of knots: the knot quandle”, Journal of Pure and Applied Algebra, 23 (1982), 37–65

[7] Yu. V. Drobotukhina, Analog polinoma Dzhonsa dlya zatseplenii v ${\mathbb R}P^3$ i obobschenie teoremy Kaufmana-Murasugi, Algebra i analiz:2 (1991), 613–630

[8] Ju. V. Drobotukhina, “Classification of links in ${\mathbb R}P^3$ with at most six crossings”, Advances in Soviet Mathematics, 18:1 (1994), 87–121

[9] S. V. Matveev, “Distributivnye gruppoidy v teorii uzlov”, Matematicheskii sbornik, 119(161):1 (1981), 78–88