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Spherical 3-manifold
In mathematics, a spherical 3-manifold M is a prime, orientable, closed 3-manifold of the form
- M = S3 / Γ
where Γ is a finite subgroup of SO(4) acting freely by rotations on the 3-sphere S3. Spherical 3-manifolds are sometimes called elliptic 3-manifolds.
A spherical 3-manifold has a finite fundamental group isomorphic to Γ itself. The elliptization conjecture states that if a 3-manifold has finite fundamental group, then it is a spherical manifold.
The manifolds S3 / Γ with Γ cyclic are precisely the 3-dimensional lens spaces. Other examples of spherical manifolds include the Poincaré sphere. A lens space is not determined by its fundamental group, but any other spherical manifold is.
03-10-2013 05:06:04
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details