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Then-equivalence of knots and invariants of finite degree

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Abstract

A series of new equivalence relations for classical knots is introduced. Factorization of the semigroup of knots converts it into a finitely generated Abelian group. The n-equivalence class of a knot is its universal invariant of degree n. The techniques described can be successfully applied in a considerably more general situation. Bibliography: 3 titles.

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Literature Cited

  1. M. Gusarov, “A new form of the Conway-Jones polynomial of oriented links,”Zap. Nauchn. Semin. LOMI,193, 4–9 (1991).

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  2. Y. Ohyama, “A new numerical invariant of knots induced from their diagrams,”Topology Appl.,37, 259–255 (1990).

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  3. M. Yamamoto, “Knots as spatial embeddings of the complete graph on four vertices,”Topology Appl.,38 (1991).

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Authors
  1. M. N. Gusarov
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Additional information

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 208, 1993, pp. 153–173.

Translated by O. A. Ivanov.

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Gusarov, M.N. Then-equivalence of knots and invariants of finite degree. J Math Sci 81, 2549–2561 (1996). https://doi.org/10.1007/BF02362425

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  • DOI: https://doi.org/10.1007/BF02362425

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