An invariant of links in a thickened torus
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 11, Tome 372 (2009), pp. 5-18 Cet article a éte moissonné depuis la source Math-Net.Ru

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For links in a thickened torus, we construct a polynomial invariant depending on three variables. The construction involves Kauffman's formal theory based on Dehn's presentation of the group of a knot. Certain properties of the invariant are established, and a theorem about a Conway type relation is proved. Bibl. – 10 titles.
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M. V. Zenkina; V. O. Manturov. An invariant of links in a thickened torus. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 11, Tome 372 (2009), pp. 5-18. http://geodesic.mathdoc.fr/item/ZNSL_2009_372_a0/

[1] S. A. Grishanov, V. R. Meshkov, V. A. Vassiliev, “Recognizing textile structures by finite type knot invariants”, J. Knot Theory Ramif., 18 (2009), 209–245 | DOI | MR

[2] S. A. Grishanov, V. A. Vassiliev, “Invariants of links in 3-manifolds and splitting problem of textile structures”, J. Knot Theory Ramif. (to appear)

[3] L. H. Kauffman, Formal Knot Theory, Math. Notes, 30, Princeton Univ. Press, Princeton, New Jersey, 1983 | MR | Zbl

[4] L. H. Kauffman, “Virtual knot theory”, Eur. J. Comb., 20:7 (1999), 662–690 | DOI | MR

[5] V. O. Manturov, “Gomologii Khovanova s proizvolnymi koeffitsientami dlya virtualnykh uzlov”, Izv. RAN. Ser. matem., 71:5 (2007), 111–148 | DOI | MR | Zbl

[6] V. O. Manturov, Teoriya uzlov, RKhD, M.–Izhevsk, 2005

[7] V. O. Manturov, “O polinomialnykh invariantakh virtualnykh zatseplenii”, Trudy Mosk. Mat. Obsch., 65, 2004, 175–200 | MR

[8] P. Ozsváth, Z. Szabó, “Heegaard diagrams and Floer homology”, Int. Congress Math., Vol. II, Europ. Math. Soc., Zürich, 2006, 1083–1099 | MR | Zbl

[9] T. Ohtsuki, Quantum Invariants, World Sci., Singapore, 2002 | MR | Zbl

[10] J. A. Rasmussen, Floer homology and knot complements, PhD Thesis, Harvard Univ., Cambridge, 2003 ; arxiv: math/0306378[math.GT] | MR