On intersection of two embedded spheres in 3-space
Geometric Topology
2015-03-17 v9 Combinatorics
Metric Geometry
Abstract
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.
Cite
@article{arxiv.1012.0925,
title = {On intersection of two embedded spheres in 3-space},
author = {Alexey Rukhovich},
journal= {arXiv preprint arXiv:1012.0925},
year = {2015}
}
Comments
English: 7 pages, 4 figures; Russian: 6 pages, 5 figures; minor changes