On intersection of two embedded spheres in 3-space
Abstract
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 = x1,x2,...,xn, y = y1,y2,...,yn of positive integers, for existence of 2-dimensional polyhedra f,g in R3 homeomorphic to the sphere and such that * f-g has n connected components, of which the i-th one has xi neighbors in f and * g-f has n connected components, of which the i-th one has yi 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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