A228038 Dimensions in which nonzero Arf-Kervaire invariants exist.

2, 6, 14, 30, 62

Offset

2,1

Comments

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. Thus either the sequence is complete or it has one additional term.

Connections with string theory (see Google link) are speculative.

Links

Table of n, a(n) for n=2..6.

M. A. Hill, M. J. Hopkins and D. C. Ravenel, On the non-existence of elements of Kervaire invariant one, arXiv:0908.3724 [math.AT], 2009-2015.

Links via Google, Hill, Hopkins, Ravenel and string theory

V. P. Snaith, A history of the Arf-Kervaire invariant problem, Notices Amer. Math. Soc., 60 (No. 8, 2013), 1040-1047.

Formula

2^n - 2 for n = 2, 3, 4, 5, 6.

Crossrefs

Cf. A228689, A000918.

Sequence in context: A260058 A331699 A327048 * A122958 A122959 A095121

Adjacent sequences: A228035 A228036 A228037 * A228039 A228040 A228041

Keyword

nonn,fini,more

Author

Jonathan Sondow, Sep 01 2013

Status

approved