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This article is cited in 12 scientific papers (total in 12 papers)
Three-Page Approach to Knot Theory. Universal Semigroup
I. A. Dynnikov M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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.
Received: 12.10.1999
Citation:
I. A. Dynnikov, “Three-Page Approach to Knot Theory. Universal Semigroup”, Funktsional. Anal. i Prilozhen., 34:1 (2000), 29–40; Funct. Anal. Appl., 34:1 (2000), 24–32
Linking options:
https://www.mathnet.ru/eng/faa280https://doi.org/10.4213/faa280 https://www.mathnet.ru/eng/faa/v34/i1/p29
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Abstract page: | 685 | Full-text PDF : | 331 | References: | 64 | First page: | 3 |
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