Intrinsic linking and knotting in virtual spatial graphs

Fleming, Thomas; Mellor, Blake

doi:10.2140/agt.2007.07.583

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Intrinsic linking and knotting in virtual spatial graphs

Thomas Fleming and Blake Mellor

Algebraic & Geometric Topology 7 (2007) 583–601

DOI: 10.2140/agt.2007.07.583

arXiv: math.GT/0606231

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.

Keywords

spatial graph, intrinsically linked, intrinsically knotted, virtual knot

Mathematical Subject Classification 2000

Primary: 05C10

Secondary: 57M27

References

Publication

Received: 19 June 2006

Accepted: 13 March 2007

Published: 10 May 2007

Authors

Thomas Fleming
Department of Mathematics University of California, San Diego La Jolla, CA 92093-0112

Blake Mellor
Mathematics Department Loyola Marymount University Los Angeles, CA 90045-2659
http://myweb.lmu.edu/bmellor

Volume 7, issue 2 (2007)