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Full-Text Articles in Physical Sciences and Mathematics
Cyclic Maps In Rational Homotopy Theory, Gregory Lupton, Sam Smith
Cyclic Maps In Rational Homotopy Theory, Gregory Lupton, Sam Smith
Mathematics and Statistics Faculty Publications
The notion of a cyclic map g:A→X is a natural generalization of a Gottlieb element in π n (X). We investigate cyclic maps from a rational homotopy theory point of view. We show a number of results for rationalized cyclic maps which generalize well-known results on the rationalized Gottlieb groups.
Homotopy Actions, Cyclic Maps And Their Duals, Martin Arkowitz, Gregory Lupton
Homotopy Actions, Cyclic Maps And Their Duals, Martin Arkowitz, Gregory Lupton
Mathematics and Statistics Faculty Publications
An action of A on X is a map F: AxX to X such that F|_X = id: X to X. The restriction F|_A: A to X of an action is called a cyclic map. Special cases of these notions include group actions and the Gottlieb groups of a space, each of which has been studied extensively. We prove some general results about actions and their Eckmann-Hilton duals. For instance, we classify the actions on an H-space that are compatible with the H-structure. As a corollary, we prove that if any two actions F and F' of A on X …