In what became one of the so-called "Millenium Problems", Henri Poincare conjectured that the 3-sphere is unique in being the simplest 3-dimensional manifold. (More info here.) It is likely that the conjecture has now been proved by the St. Petersburg mathematician Grigori Perelman, who stands to earn $1 million for having solved one of the millenium problems.
Poincare himself proved that the 2-sphere is the simplest manifold in 2 dimensions, respectively. Given that, by 1982, Poincare's Conjecture was proved for n-spheres, where n is greater than or equal to 4, was it at all likely that it would fail to hold for n=3? That is, did we have had some prior justification in believing Poincare's Conjecture to be true, given that we knew that it held for all n other than n=3?
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