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Knots and the Bracket Calculus

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Abstract

In this paper, we introduce a way of encoding links (long links). This ways leads to a combinatorial representation of links by words in a given finite alphabet. We prove that the link semigroup is isomorphic to some algebraically defined semigroup with a simple system of relations. Thus, knot theory is represented as a bracket calculus: the link recognition problem is reduced to a recognition problem in this semigroup.

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References

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Authors and Affiliations

  1. Chair of Differential Geometry and Applications, Mechanical and Mathematical Department, Moscow State University, 119899, Moscow, Russia

    V. O. Manturov

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  1. V. O. Manturov
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Manturov, V.O. Knots and the Bracket Calculus. Acta Applicandae Mathematicae 74, 293–336 (2002). https://doi.org/10.1023/A:1021154925574

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  • DOI: https://doi.org/10.1023/A:1021154925574

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