Geometric approach to stable homotopy groups of spheres. I. The Hopf invariant

Abstract

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.

References in corpus (4)

• On the non-existence of elements of Kervaire invariant one
• Geometric approach towards stable homotopy groups of spheres. The Hopf invariant
• Geometric approach towards stable homotopy groups of spheres. The Kervaire invariant II
• Geometric approach to stable homotopy groups of spheres, III. Abelian, cyclic and quaternionic structure for mappings with singularities

Cited by in corpus (2)

• Kairvaire Problems in Stable Homotopy Theory
• $K$-theory of $S^7/Q_8$ and a counterexample to a result of P.M. Akhmet'ev