Download PDFOpen PDF in browserA Practical Approach to the Homotopy Groups of SpheresEasyChair Preprint 95483 pages•Date: January 5, 2023AbstractIn the paper we utilize correspondence between the ith homotopy group of (r+1)sphere and the ith 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 HiltonMilnor splittings, Necklace polynomials, Wedge sum, configuration space, homotopy groups, spheres
