The Homotopy Set of the Axes of Pairings

Source abstract

Varadarajan [13] named a map f : A → X a cyclic map when there exists a map F : X × A → X such that for the folding map ∇ X : X ∨ X → X . He defined the generalized Gottlieb set G ( A , X ) of the homotopy classes of the cyclic maps F : A → X and studied the fundamental properties of G ( A , X ) If A is a co-Hopf space, then the Varadarajan set G ( A , X ) has a group structure [13]. The group G(A,X) is a generalization of G(X) and G n (X) of Gottlieb [2,3]. Some authors studied the properties of the Varadarajan set, its dual and related topics [4, 5, 6, 7,12,15,16,17].