Abstract
A new approach to the definition of the notion of finite-degree invariants of oriented links is described. It is proved that using new transformations, which are much more general than usual, actually leads to the same theory of such invariants. Applying these general transformations we also prove that the invariants of finite degree are polynomials in the gleams if the Hopf projection of the link is fixed. Bibliography: 3 titles.
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References
M. N. Gusarov, “On then-equivalence of knots and invariants of finite degree,”Zap. Nauchn. Semin. POMI,208, 152–173 (1993).
M. N. Gusarov, “Onn-equivalence of knots and invariants of finite degree,”Adv. Sov. Math.,18, 173–192 (1994).
V. G. Turaev, “Shadow links and face models of statistical mechanics,”J. Diff. Geom.,36, 35–74 (1992)
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 141–147.
Translated by N. Yu. Netsvetaev.
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Gusarov, M.N. The behavior of invariants of finite degree under interdependent transformations of links. J Math Sci 91, 3420–3424 (1998). https://doi.org/10.1007/BF02434918
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DOI: https://doi.org/10.1007/BF02434918