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Three-page approach to knot theory. Universal semigroup

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Abstract

An explicit construction of a finitely presented semigroup whose central elements are in a one-to-one correspondence with the isotopy classes of unoriented links in the three-space is given, together with a finite presentation for the group of invertible elements of the semigroup. The group is presented by two generators and three relations. The commutator subgroup of the group is isomorphic to the braid group of infinite index. A similar construction is given for band-links. The kauffman theorems on the existence of polynomial band-link invariants satisfying some skein-relations are stated algebraically.

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Authors
  1. I. A. Dynnikov
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Additional information

This work is partially supported by Russian Foundation for Basic Research grant No. 99-01-00090.

Moscow State University. Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 34, No. 1, pp. 29–40, January–March, 2000.

Translated by I. a. Dynnikov

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Dynnikov, I.A. Three-page approach to knot theory. Universal semigroup. Funct Anal Its Appl 34, 24–32 (2000). https://doi.org/10.1007/BF02467064

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  • DOI: https://doi.org/10.1007/BF02467064

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