Abstract
In an earlier paper [E4] we introduced an algebraic structure on sets of homotopy classes [S p ×S q ;S n ], given by the reflecting product • on spheresS n , which makes these sets symmetric groupoids. In this article we determine precisely the algebraic structure of the symmetric groupoids ([S n ×S n ;S n ], •) forn ≠ 1, 3, 7.
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