spherical 3-manifold

In mathematics, a spherical 3-manifold M is a prime, orientable, closed 3-manifold of the form

M=S^3/\Gamma

where Γ is a finite subgroup of SO(4) acting freely by rotations on

S^3

. Spherical 3-manifolds are sometimes called elliptic 3-manifolds. A spherical 3-manifold has a finite fundamental group: the fundamental group of M is Γ itself. The elliptization conjecture states that if a 3-manifold has finite fundamental group, then it is a spherical manifold. The manifolds

S^3/\Gamma

with Γ cyclic are precisely the 3-dimensional lens spaces. Other examples of spherical manifolds include the Poincar sphere. A lens space is not determined by its fundamental group, but any other spherical manifold is.

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