Slide 33, “To Conclude: An Open Problem”
For each n, the oriented diffeomorphism classes of manifolds homeomorphic to Sⁿ form a semigroup under connected sum. For n ≠ 4 it is a finite abelian group (Kervaire–Milnor, with Perelman); it is trivial for n = 1, 2, 3, 5, 6, 12, 61 and non-trivial for every other n ≤ 63 except 4. The smooth analogue in dimension four remains open.
Passage details
Passage ID: poincare-conjecture:entry:milnor-spheres:v1
Source item: Slide 33, “To Conclude: An Open Problem”
Source record: milnor-four-centuries@icm-2014-slides-sha256-89cf5c46