On 3-manifolds
Abstract
It is well known that a three dimensional (closed, connected and compact) manifold is obtained by identifying boundary faces from a polyhedron P. The study of (\partial P)/~, the boundary \partial P with the polygonal faces identified in pairs leads us to the following conclusion: either a three dimensional manifold is homeomorphic to a sphere or to a polyhedron P with its boundary faces identified in pairs so that (\partial P)/~ is a finite number of internally flat complexes attached to each other along the edges of a finite graph that contains at least one closed circuit. Each of those internally flat complexes is obtained from a polygon where each side may be identified with more than one different sides. Moreover, Euler characteristic of (\partial P)/~ is equal to one and the fundamental group of (\partial P)/~ is not trivial.
Cite
@article{arxiv.math/0511457,
title = {On 3-manifolds},
author = {Sergey Nikitin},
journal= {arXiv preprint arXiv:math/0511457},
year = {2007}
}