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Consequences of the kahn–priddy theorem in homotopy and geometry
Published online by Cambridge University Press: 26 February 2010
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Much recent attention has been given to geometric representation of elements of the stable homotopy groups of spheres, π*s A particular example concerns non-singular bilinear maps ℝm+1 × ℝn+1 → ℝm+n+1−p; on restriction and normalisation these become biskew maps Sm × Sn ℝ Sm+n-p;. Now the Hopf construction ℋ applied to any map f: Sm × Sn → Sm+n-p yields
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