Depicted here are representatives for the components of the spaces of 5 and 6 move plumbers' knots. The components were enumerated using this java code and the images were created using this Mathematica notebook. To classify them, the Jones polynomial for each knot was computed using this Mathematica notebook and the Knot Theory' package.

Representatives for components of K₅

00
31 (right handed)
31 (left handed)

Representatives for components of K₆

00
31 (right handed)
31 (left handed)
41
51 (right handed)
51 (left handed)
52 (right handed)
52 (left handed)

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Department of Mathematics, University of Oregon, Eugene OR 97403
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