On transforming a spatial graph into a plane graph
On transforming a spatial graph into a plane graph
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关于将空间图转化为平面图
DOI：
10.1143/ptps.191.225
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发表时间：
2011
影响因子：
--
通讯作者：
Akio Kawauchi
中科院分区：
文献类型：
--
作者：
F. Kaneda;S.-Y. Baek;M. Ozawa;K.Edamatsu;Nobuhiko Terui;二木昭人;H.Tokunaga;Akio Kawauchi
本文是[Bussei Kenkyu 92(2009)，16]研究公告[Bussei Kenkyu 92(2009)，16]的详细修订版，它引入了空间图的复杂性，这对于将空间图(没有一次顶点)转换为平面图是有用的。我们还为每个空间图引入了相关的拓扑不变量，称为翘曲度，以及γ-Warping度和(γΓ)-Warping度。我们还将通常的结点解开数推广到每个空间图，并为每个空间图引入了相关的拓扑不变量，称为γ-解结数、Γ-解结数和(γΓ)-解结数。这些不变量被用来定义具有一阶顶点的空间图的“半拓扑”不变量，即使对于结节弧也是有意义的。
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.