Geodesic
Intrinsic linking and knotting in virtual spatial graphs
Fleming, Thomas1 ; Mellor, Blake2
1Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112
2Mathematics Department, Loyola Marymount University, Los Angeles, CA 90045-2659
Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 583-601
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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.

DOI : 10.2140/agt.2007.07.583
Keywords: spatial graph, intrinsically linked, intrinsically knotted, virtual knot

Fleming, Thomas  1   ; Mellor, Blake  2

1 Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112
2 Mathematics Department, Loyola Marymount University, Los Angeles, CA 90045-2659 
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Fleming, Thomas; Mellor, Blake. Intrinsic linking and knotting in virtual spatial graphs. Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 583-601. doi: 10.2140/agt.2007.07.583

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