## Algebraic & Geometric Topology

### Intrinsic linking and knotting in virtual spatial graphs

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 7, Number 2 (2007), 583-601.

Dates
Accepted: 13 March 2007
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796699

Digital Object Identifier
doi:10.2140/agt.2007.07.583

Mathematical Reviews number (MathSciNet)
MR2308958

Zentralblatt MATH identifier
1147.57013

#### Citation

Fleming, Thomas; Mellor, Blake. Intrinsic linking and knotting in virtual spatial graphs. Algebr. Geom. Topol. 7 (2007), no. 2, 583--601. doi:10.2140/agt.2007.07.583. https://projecteuclid.org/euclid.agt/1513796699

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