arXiv:0905.3948 Abstract | arXiv Analytics

arXiv:0905.3948 [math.GT]Abstract References Reviews Resources

The quandle and group for higher-dimensional and virtual knots

Published 2009-05-25Version 1

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.

Comments: 7 pages, 2 figures

Categories: math.GT, math.QA

Subjects: 17D99, 57R40

Keywords: virtual knots, higher-dimensional, peripheral structure, fundamental quandle, fundamental group

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