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A note on the divisibility of the Whitehead square

Haruo Minami

Abstract

We show that if we suppose n>3 and the (2n-1)-stem in the stable homotopy groups of spheres has no 2-torsion, then the Whitehead squares of the identity maps of (2n+1) and (4n+3)-spheres are divisible by 2. Applying the result of G. Wang and Z. Xu on the 61-stem in the stable homotopy groups of spheres, we find that the Kervaire invariant one elements in dimensions 62 and 126 exist.

A note on the divisibility of the Whitehead square

Abstract

We show that if we suppose n>3 and the (2n-1)-stem in the stable homotopy groups of spheres has no 2-torsion, then the Whitehead squares of the identity maps of (2n+1) and (4n+3)-spheres are divisible by 2. Applying the result of G. Wang and Z. Xu on the 61-stem in the stable homotopy groups of spheres, we find that the Kervaire invariant one elements in dimensions 62 and 126 exist.

Paper Structure

This paper contains 2 sections, 40 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem

Theorems & Definitions (5)

  • proof
  • proof
  • proof
  • proof : Proof of Theorem
  • Remark