A proof for it involving the use of (*) k-handles was developed by Smale and the Kirby-Siebenmann invariant was central to Freedmen's Fields medal winning proof for the n equals 4 case.
It is a special case of the Thurston elliptization conjecture and Whitehead developed his namesake prime link while trying to prove this statement. A proof for it involving the use of (*) k-handles was developed by Smale and the Kirby-Siebenmann invariant was central to Freedmen's Fields medal winning proof for the n equals 4 case. For 10 points, name this conjecture, which states that a compact n-manifold is equivalent to the n-sphere if it has the same homotopy groups.
It is a special case of the Thurston elliptization conjecture and Whitehead developed his namesake prime link while trying to prove this statement.
{Poincaré} conjecture