ar X iv : m at h / 05 11 45 7 v 5 [ m at h . G M ] 6 F eb 2 00 6 On 3 - manifolds
نویسنده
چکیده
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 (∂P )/ ∼, the boundary ∂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 (∂P )/ ∼ is a two dimensional CW -complex. (∂P )/ ∼ is a finite number of two dimensional cells attached to each other along the edges of a finite graph that contains at least one closed circuit. Each of those cells is obtained from a polygon where each side may be identified with one or more other different sides. Moreover, Euler characteristic of (∂P )/ ∼ is equal to one and the fundamental group of (∂P )/ ∼ is not trivial.
منابع مشابه
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تاریخ انتشار 2008