10 citations · 36 across the 15 of their papers we have counts for
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A generalized Kervaire Problem in stable homotopy groups of spheres
Petr M. Akhmet'ev
We will give an elementary self-contained description of the Mahowald element in the stable homotopy group of spheres , . Using this construction, we prove that a…
Geometric approach to stable homotopy groups of spheres II; Arf-Kervaire Invariants
Petr M. Akhmet'ev
The Kervaire Invariant 1 Problem until recently was an open problem in algebraic topology. Hill-Hopkins-Ravenel theorem clams a negative solution of the problem for all dimensions…
Kairvaire Problems in Stable Homotopy Theory
Petr Akhmet'ev
The Kervaire Problem is an unsolved problem in Stable Homotopy Theory. The first interesting example is in dimension . There exists a closed stably-parallelizable manifold $\ti…
Geometric approach to stable homotopy groups of spheres II. The Kervaire invariant
Petr M. Akhmet'ev
A solution to the Kervaire invariant problem is presented. We introduce the concepts of abelian structure on skew-framed immersions, bicyclic structure on --framed imme…
Geometric approach to stable homotopy groups of spheres, III. Abelian, cyclic and quaternionic structure for mappings with singularities
Petr M. Akhmet'ev
Collection of (equivariant) -mappings admitting a relative abelian, cyclic, quaternionic, bicyclic, and quaternionic-cyclic structures are constructed.
Geometric approach to stable homotopy groups of spheres. I. The Hopf invariant
Petr M. Akhmet'ev
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 alter…
Geometric approach towards stable homotopy groups of spheres. The Hopf invariant
Petr M. Akhmet'ev
We develop a geometric approach to stable homotopy groups of spheres in the spirit of the work of Pontrjagin and Rokhlin. A new proof of the Hopf Invariant One Theorem by J.F.Adams…