cp's OEIS Frontend

A228038 Dimensions in which nonzero Arf-Kervaire invariants exist.

%I A228038 #34 May 09 2025 16:19:46
%S A228038 2,6,14,30,62,126
%N A228038 Dimensions in which nonzero Arf-Kervaire invariants exist.
%C A228038 Hill, Hopkins, and Ravenel (2009) proved that nonzero Arf-Kervaire invariants exist only in dimensions 2^n - 2 for n = 2, 3, 4, 5, 6, and possibly 7, that is, in dimensions 2, 6, 14, 30, 62 and possibly 126.
%C A228038 The preprint by Lin, Wang, and Xu asserts that nonzero Arf-Kervaire invariants exist in dimension 126.
%H A228038 J. Baez, <a href="https://golem.ph.utexas.edu/category/2009/04/kervaire_invariant_one_problem.html">‘Kervaire Invariant One Problem’ Solved</a>, The n-Category Café (blog), April 2009.
%H A228038 M. A. Hill, M. J. Hopkins and D. C. Ravenel, <a href="http://arxiv.org/abs/0908.3724">On the non-existence of elements of Kervaire invariant one</a>, arXiv:0908.3724 [math.AT], 2009-2015.
%H A228038 Erica Klarreich, <a href="https://www.quantamagazine.org/dimension-126-contains-strangely-twisted-shapes-mathematicians-prove-20250505/">Dimension 126 Contains Strangely Twisted Shapes, Mathematicians Prove</a>, Quanta Magazine, May 2025.
%H A228038 Weinan Lin, Guozhen Wang, and Zhouli Xu, <a href="https://arxiv.org/abs/2412.10879">On the Last Kervaire Invariant Problem</a>, arXiv:2412.10879 [math.AT], 2024-2025.
%H A228038 V. P. Snaith, <a href="http://www.ams.org/notices/201308/rnoti-p1040.pdf">A history of the Arf-Kervaire invariant problem</a>, Notices Amer. Math. Soc., 60 (No. 8, 2013), 1040-1047.
%H A228038 Wikipedia, <a href="https://en.wikipedia.org/wiki/Kervaire_invariant">Kervaire invariant</a>
%F A228038 a(n) = 2^n - 2 for n = 2, 3, 4, 5, 6, 7.
%Y A228038 Cf. A228689, A000918.
%K A228038 nonn,fini,full
%O A228038 2,1
%A A228038 _Jonathan Sondow_, Sep 01 2013
%E A228038 a(7) from _David Radcliffe_, May 09 2025