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 non-terminating. We also provide several examples of intrinsically virtually linked and knotted graphs. As a byproduct, we introduce the {\it virtual unknotting number} of a knot, and show that any knot with non-trivial Jones polynomial has virtual unknotting number at least 2.

13 pages, 13 figures

Cited by in corpus (5)

• Classical and Virtual Pseudodiagram Theory and New Bounds on Unknotting Numbers and Genus
• An Introduction to Virtual Spatial Graph Theory
• Virtually Symmetric representations and marked Gauss diagrams
• The generalized Yamada polynomials of virtual spatial graphs
• The forbidden number of a knot