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2007 Intrinsic linking and knotting in virtual spatial graphs
Thomas Fleming, Blake Mellor
Algebr. Geom. Topol. 7(2): 583-601 (2007). DOI: 10.2140/agt.2007.07.583

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 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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Thomas Fleming. Blake Mellor. "Intrinsic linking and knotting in virtual spatial graphs." Algebr. Geom. Topol. 7 (2) 583 - 601, 2007. https://doi.org/10.2140/agt.2007.07.583

Information

Received: 19 June 2006; Accepted: 13 March 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1147.57013
MathSciNet: MR2308958
Digital Object Identifier: 10.2140/agt.2007.07.583

Subjects:
Primary: 05C10
Secondary: 57M27

Rights: Copyright © 2007 Mathematical Sciences Publishers

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