Knot quandle decompositions

Alessia Cattabriga; Eva Horvat

doi:10.1007/s00009-020-01530-6

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arXiv · 1901.10996

Knot quandle decompositions

Alessia Cattabriga·Eva Horvat

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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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Alessia Cattabriga, Eva Horvat. 2019-01-30. Knot quandle decompositions. https://doi.org/10.1007/s00009-020-01530-6

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