Mathematics – Metric Geometry
Scientific paper
2011-11-03
Mathematics
Metric Geometry
This paper has been withdrawn by the author because it is a part of article arxiv:1012.0925; this part was submitted by mistak
Scientific paper
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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