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関連
http://en.wikipedia.org/wiki/Homology_sphere
Homology sphere

Poincaré homology sphere
The Poincaré homology sphere (also known as Poincaré dodecahedral space) is a particular example of a homology sphere.
Being a spherical 3-manifold, it is the only homology 3-sphere (besides the 3-sphere itself) with a finite fundamental group.
Its fundamental group is known as the binary icosahedral group and has order 120.
This shows the Poincaré conjecture cannot be stated in homology terms alone.