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Geometric approach to stable homotopy groups of spheres. I. The Hopf invariant by Akhmet'ev, Petr M. is a scholarly article available to read on EtoBox.

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A geometric approach to the stable homotopy groups of spheres is developed in this paper, based on the Pontryagin-Thom construction. The task of this approach is to obtain an alternative proof of the Hill-Hopkins-Ravenel theorem [H-H-R] on Kervaire invariants in all dimensions, except, possibly, a finite number of dimensions. In the framework of this approach, the Adams theorem on the Hopf invariant is studied, for all dimensions with the exception of 15, 31, 63, 127. The new approach is based on the methods of geometric topology.

Author

Akhmet'ev, Petr M.

Published

2010

Language

EN