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Knot Quandle Decompositions

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Abstract

We show that the fundamental quandle defines a functor from the oriented tangle category to a suitably defined quandle category. Given a tangle decomposition of a link L, the fundamental quandle of L may be obtained from the fundamental quandles of tangles. We apply this result to derive a presentation of the fundamental quandle of periodic links, composite knots and satellite knots.

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Authors and Affiliations

  1. Department of Mathematics, University of Bologna, Piazza di Porta, San Donato 5, 40126, Bologna, Italy

    A. Cattabriga

  2. Faculty of Education, University of Ljubljana, Kardeljeva ploščad 16, 1000, Ljubljana, Slovenia

    E. Horvat

Authors
  1. A. Cattabriga
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  2. E. Horvat
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Correspondence to A. Cattabriga.

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The first author was supported by the “National Group for Algebraic and Geometric Structures, and their Applications” (GNSAGA-INdAM) and University of Bologna, funds for selected research topics. The second author was supported by the Slovenian Research Agency Grant N1-0083.

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Cattabriga, A., Horvat, E. Knot Quandle Decompositions. Mediterr. J. Math. 17, 98 (2020). https://doi.org/10.1007/s00009-020-01530-6

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  • DOI: https://doi.org/10.1007/s00009-020-01530-6

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