On the Homotopy Groups of the Union of Spheres

  title={On the Homotopy Groups of the Union of Spheres},
  author={Peter J. Hilton},
  journal={Journal of The London Mathematical Society-second Series},
  • P. Hilton
  • Published 1 April 1955
  • Mathematics
  • Journal of The London Mathematical Society-second Series
Let 8( be a sphere of dimension r,+ l, rt^ 1, i = 1, ..., h, and let T be the union of the spheres Sv ..., Sk, with a single common point. Then T serves as a universal example for homotopy constructions (see [1]). The object of this paper is to compute the group irn{T), n > 1, as a direct sum of homotopy groups of spheres of appropriate dimensions^:. Each summand is embedded in TTn{T) by a certain multiple Whitehead product; the products which appear will be called basic products and will now… 

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