Geodesic
On the nonexistence of elements of Kervaire invariant one
M. A. Hill1 ; M. J. Hopkins2 ; D. C. Ravenel3
1 University of Virginia, Charlottesville, VA
2 Harvard University, Cambridge, MA
3 University of Rochester, Rochester, NY
Annals of mathematics, Tome 184 (2016) no. 1, pp. 1-262.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We show that the Kervaire invariant one elements $\theta_{j}\in\pi_{2^{j+1}-2}S^{0}$ exist only for $j\le 6$. By Browder’s Theorem, this means that smooth framed manifolds of Kervaire invariant one exist only in dimensions $2$, $6$, $14$, $30$, $62$, and possibly $126$. Except for dimension $126$ this resolves a longstanding problem in algebraic topology.
DOI : 10.4007/annals.2016.184.1.1

M. A. Hill 1 ; M. J. Hopkins 2 ; D. C. Ravenel 3

1 University of Virginia, Charlottesville, VA
2 Harvard University, Cambridge, MA
3 University of Rochester, Rochester, NY 
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M. A. Hill; M. J. Hopkins; D. C. Ravenel. On the nonexistence of elements of Kervaire invariant one. Annals of mathematics, Tome 184 (2016) no. 1, pp. 1-262. doi : 10.4007/annals.2016.184.1.1. http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.184.1.1/

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