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.
Knot Quandle Decompositions / Cattabriga A.; Horvat E.. - In: MEDITERRANEAN JOURNAL OF MATHEMATICS. - ISSN 1660-5446. - ELETTRONICO. - 17:3(2020), pp. 98.1-98.22. [10.1007/s00009-020-01530-6]
Knot Quandle Decompositions
Cattabriga A.
;
2020
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.File in questo prodotto:
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