A Practical Approach to the Homotopy Groups of Spheres

EasyChair Preprint 9548

Abstract

In the paper we utilize correspondence between the i-th homotopy group of (r+1)-sphere and the i-th homotopy group of the wedge sum of i (r+1)-spheres based on Hilton's theorem (the homotopy groups of such wedge sums consolidate all information about homotopy groups of spheres). This leads to a practical method for computing the homotopy groups of spheres. Moreover, it reduces the computation of the homotopy groups of (r+1)-sphere to a combinatorial group theory question.

Keyphrases: Bouquet of spheres, Freudenthal suspension theorem, Hilton's theorem, James and Hilton-Milnor splittings, Necklace polynomials, Wedge sum, configuration space, homotopy groups, spheres

@booklet{EasyChair:9548,
  author    = {Valerii Sopin},
  title     = {A Practical Approach to the Homotopy Groups of Spheres},
  howpublished = {EasyChair Preprint 9548},
  year      = {EasyChair, 2023}}