A191783 Numbers k such that the topological k-sphere has a unique differentiable structure up to diffeomorphism.

1, 2, 3, 5, 6, 12, 56, 61

Offset: 1

Author

N. J. A. Sloane, Jun 25 2011

Keywords

• nonn
• more
• hard
• nice

Comments

Whether 4 is a term is an open question. - Andrey Zabolotskiy, Feb 02 2018

Except (possibly) for k=4, these are the numbers k such that A001676(k)=1. - Jeppe Stig Nielsen, May 22 2019

The list in Milnor's paper (p. 807, A358290) does not include the term 56 because it was only discovered later that it is actually a term of this list, see Wang & Xu, Theorem 1.14. - Andrey Zabolotskiy, Nov 29 2022

Dimensions without exotic spheres. - Charles R Greathouse IV, Dec 22 2022

Links

• Brady Haran and Ciprian Manolescu, The Puzzling Fourth Dimension (and exotic shapes), Numberphile video (2022).
• John W. Milnor, Differential Topology Forty-six Years Later, Notices Amer. Math. Soc. 58 (2011), 804-809.
• Guozhen Wang and Zhouli Xu, The triviality of the 61-stem in the stable homotopy groups of spheres, Annals of Mathematics, 186 (2017), 501-580; arXiv:1601.02184 [math.AT], 2016-2017.

Crossrefs

Cf. A001676, A358290.

Extensions

Definition rewritten by Jeppe Stig Nielsen, May 22 2019

The term a(7) = 56 inserted by Andrey Zabolotskiy, Nov 27 2022