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The quandle and group for higher-dimensional and virtual knots

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arxiv 0905.3948 v1 pith:LYTVRZOQ submitted 2009-05-25 math.GT math.QA

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keywords groupquandlefundamentalknotknotsperipheralstructurevirtual
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Joyce has shown that the fundamental quandle of a classical knot can be derived from consideration of the fundamental group and the peripheral structure of the knot, and also that the group and much of the peripheral structure can be recovered from the quandle. We generalize these results to arbitrary dimensions, and also to virtual and welded knots and arcs.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots

    math.GT 2026-08 accept novelty 7.0 of 10

    There are oriented 2-knots with isomorphic fundamental groups, semilinearly isomorphic second homotopy modules, and isomorphic quandles, but inequivalent first Postnikov invariants.

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