On linear graphs in 3-sphere
On linear graphs in 3-sphere
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关于 3 球面的线性图
DOI：
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发表时间：
1970
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通讯作者：
Shin’ichi Suzuki
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文献类型：
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作者：
Shin’ichi Suzuki
在本文中，我们工作在分段线性范畴，由单纯复形和分段线性映射。用（PcM）表示一对复形，使得M具有任意但固定的定向，如果M是可定向的，且P作为子复形嵌入M。K表示所有连通的有限一维复形的集合。然后，对于K^K，我们称（KaS）为三维球面S中的线性图，或简称为图。本文的目的是对{（KaS）|K^K}的等价关系，我们称之为邻域同余。我们将在{（KaS）K ∈ K}中引入一个合成运算V，使得图的邻域同余类形成一个交换半群，并给出下面的结果作为纽结[14]和链环[8]的推广.
Throughout this paper we work in the piecewise-linear category, consisting of simplicial complexes and piecewise-linear maps. By (PcM) we denote a pair of complexes such that M has an arbitrary but fixed orientation if M is orientable and P is embedded as a subcomplex in M. K denotes a set of all connected finite 1-dimensional complexes. Then, for K^Kwe will call (KaS) a linear graph, or simply graph, in a 3-dimensional sphere S. The purpose of the paper is to classify {(KaS)| K^K} by an equivalence relation, which we will call a neighborhood-congruence. We will introduce a operation V of composition in {(KaS)K£ΞK} so that neighborhoodcongruence classes of graphs form a commutative semi-group, and give the following as generalization of knots [14] and links [8].