三维空间中两个嵌入球面的交
On intersection of two embedded spheres in 3-space
摘要：
这篇文章被文章arxiv.1012.0925所覆盖我们研究了3-空间中两个没有自交的多面体球体的相交。我们找到了序列x = x_1，x_2，.的充要条件，x_n，y = y_1，y_2，.，y_n为正整数，证明了在R^3中存在与球面同胚的2维多面体f，g，使得 * f-g有n个连通分支，其中第i个连通分支在f中有x_i个近邻，* g-f有n个连通分支，其中第i个连通分支在g中有y_i个近邻.类似地，我们研究了三维空间中三个不自相交的多面体球面的相交问题。俄语版面向对数学感兴趣的高中教师和学生。
英文摘要：
This article is covered by the article arxiv.1012.0925 We study intersection of two polyhedral spheres without self-intersections in 3-space. We find necessary and sufficient conditions on sequences x = x_1,x_2,...,x_n, y = y_1,y_2,...,y_n of positive integers, for existence of 2-dimensional polyhedra f,g in R^3 homeomorphic to the sphere and such that * f-g has n connected components, of which the i-th one has x_i neighbors in f and * g-f has n connected components, of which the i-th one has y_i neighbors in g. Analogously we study intersection of three polyhedral spheres without self-intersections in 3-space. Russian version is accessible to high-school teachers and students interested in mathematics.
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