119 research outputs found
Intrinsic linking and knotting of graphs in arbitrary 3-manifolds
We prove that a graph is intrinsically linked in an arbitrary 3-manifold M if
and only if it is intrinsically linked in S^3. Also, assuming the Poincare
Conjecture, we prove that a graph is intrinsically knotted in M if and only if
it is intrinsically knotted in S^3.Comment: This is the version published by Algebraic & Geometric Topology on 9
August 200
Intrinsic Linking and Knotting in Virtual Spatial Graphs
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.Comment: 13 pages, 13 figure
Many, many more intrinsically knotted graphs
We list more than 200 new examples of minor minimal intrinsically knotted
graphs and describe many more that are intrinsically knotted and likely minor
minimal.Comment: 19 pages, 16 figures, Appendi
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