Regular projections of graphs with at most three double points

Details Regular projections of graphs with at most three double points Regular projections of graphs with at most three double points

2008-08-29

arxiv.org/abs/0808.4027v3

Mathematics

Geometric Topology

16 pages, 31 figures

Scientific paper

A generic immersion of a planar graph into the 2-space is said to be knotted if there does not exist a trivial embedding of the graph into the 3-space obtained by lifting the immersion with respect to the natural projection from the 3-space to the 2-space. In this paper we show that if a generic immersion of a planar graph is knotted then the number of double points of the immersion is more than or equal to three. To prove this, we also show that an embedding of a graph obtained from a generic immersion of the graph (does not need to be planar) with at most three double points is totally free if it contains neither a Hopf link nor a trefoil knot.

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