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A Practical Approach to the Homotopy Groups of Spheres

EasyChair Preprint no. 9548

3 pagesDate: January 5, 2023

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

BibTeX entry
BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:
@Booklet{EasyChair:9548,
  author = {Valerii Sopin},
  title = {A Practical Approach to the Homotopy Groups of Spheres},
  howpublished = {EasyChair Preprint no. 9548},

  year = {EasyChair, 2023}}
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