On 3-manifolds

Sergey Nikitin

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arXiv · math/0511457

On 3-manifolds

Sergey Nikitin

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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.

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Sergey Nikitin. 2006-02-06. On 3-manifolds. https://arxiv.org/abs/math/0511457

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