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Comment Re:Summary of the Poincare conjecture is inaccurat (Score 1) 117

Excuse me for replying to my own post. I should also mention that Poincaré's conjecture was not about 'a method for determining whether a three-dimensional manifold is a spherical'. It is simply the question of whether there are non-spheres in 3d which have all loops contractible (for a more accurate description, see the parent). The question about methods/algorithms for determining whether or not something is a 3-sphere is in itself very interesting though.

Comment Summary of the Poincare conjecture is inaccurate (Score 2, Informative) 117

As someone who's job involves research into geometry and topology, I would like to point out that the summary is wrong in a couple of places. The Poincare conjecture states (in simple terms) that:

Any closed smooth three dimensional space ('manifold') without boundary where all loops can be contracted to a point is 'homeomorphic' (essentially the same as) the three dimensional sphere (that is, the unit sphere in 4 dimensions).

The words "homologous" and "boundless" have little/nothing to do with it.

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