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Cocyclic Quasoid Knot Invariants

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Abstract

We describe some method that associates two chain complexes to every X and every mapping Q: X × X × X → X satisfying a few conditions motivated by Reidemeister moves. These complexes differ by boundary homomorphisms: For one complex, the boundary homomorphism is the difference of two operators; and for the other, their sum. We prove that each element of the third cohomology group of these complexes correctly defines an invariant of oriented links. We provide the results of calculations of cohomology groups for all various mappings Q on sets of order at most 4.

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Authors and Affiliations

  1. Chelyabinsk State University, Chelyabinsk, Russia

    Ph. G. Korablev

  2. Krasovskii Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Ph. G. Korablev

Authors
  1. Ph. G. Korablev
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Correspondence to Ph. G. Korablev.

Additional information

Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 2, pp. 344–366.

The author was supported by the Russian Foundation for Basic Research (Grant 17-01-00690) and the Foundation for Promising Research of Chelyabinsk State University.

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Korablev, P.G. Cocyclic Quasoid Knot Invariants. Sib Math J 61, 271–289 (2020). https://doi.org/10.1134/S003744662002010X

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  • DOI: https://doi.org/10.1134/S003744662002010X

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