On Transforming a Spatial Graph into a Plane Graph
Akio Kawauchi · Progress of Theoretical Physics Supplement · 2011
This article is a revised detailed version of the research announcement [Bussei Kenkyu 92 (2009), 16] introducing a complexity of a spatial graph, which is useful to transform a spatial graph (without degree one vertices) into a plane graph. We also introduce related topological invariants for every spatial graph, called the warping degree, and γ-warping degree and (γΓ)-warping degree. We also generalize the usual unknotting number of a knot to every spatial graph and introduce related topological invariants for every spatial graph, called the γ-unknotting number, Γ-unknotting number and (γΓ)-unknotting number. These invariants are used to define “semi-topological” invariants for a spatial graph with degree one vertices, meaningful even for a knotted arc.