Intrinsic Linking and Knotting in Virtual Spatial Graphs

Thomas Fleming; Blake Mellor

doi:10.2140/agt.2007.07.583

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Intrinsic Linking and Knotting in Virtual Spatial Graphs

Thomas Fleming·Blake Mellor

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Abstract

We introduce a notion of intrinsic linking and knotting for virtual spatial graphs. Our theory gives two filtrations of the set of all graphs, allowing us to measure, in a sense, how intrinsically linked or knotted a graph is; we show that these filtrations are descending and non-terminating. We also provide several examples of intrinsically virtually linked and knotted graphs. As a byproduct, we introduce the {\it virtual unknotting number} of a knot, and show that any knot with non-trivial Jones polynomial has virtual unknotting number at least 2.

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Thomas Fleming, Blake Mellor. 2006-06-09. Intrinsic Linking and Knotting in Virtual Spatial Graphs. https://doi.org/10.2140/agt.2007.07.583

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