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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 nonterminating. We also provide several examples of intrinsically virtually linked and knotted graphs. As a byproduct, we introduce the virtual unknotting number of a knot, and show that any knot with nontrivial Jones polynomial has virtual unknotting number at least 2.

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Recommended Citation

Fleming, T. and B. Mellor, 2007: Intrinsic Linking and Knotting in Virtual Spatial Graphs. Algebr. Geom. Topol., 7, 583-601.