William Thurston's ellipticism suggests that a closed 3-species with a finite fundamental group is spherical, that is, this 3-variety has a Riemann metric with a constant positive section curve. A 3-variety with such a metric is covered by the 3-atmosphere, in addition, the groups of overhanging transformations are 3-atmosphere isometries.
This means that if the original 3 variety actually has a trivial fundamental group, it is homeomorphic to the 3-atmosphere (via the overlay image). The ellipticism is a special case of Thurston's perception of admiration, which was proven by Grigori Perelman in 2003. This evidence also proved the presumption of Poincaré, because Thurston ellipticality is logically equivalent to two simpler suspicions: the presumption of Poincaré and the spherical space formality.
For proof of assumptions, see the in the articles about Thurston's perceptions of admissions or suspicion of Poincaré
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