A Rational Obstruction to Be a Gottlieb Map
نویسنده
چکیده
We investigate Gottlieb maps, which are maps f : E → B that induce the maps between the Gottlieb groups πn(f)|Gn(E) : Gn(E) → Gn(B) for all n, from a rational homotopy theory point of view. We will define the obstruction group O(f) to be a Gottlieb map and a numerical invariant o(f). It naturally deduces a relative splitting of E in certain cases. We also illustrate several rational examples of Gottlieb maps and non-Gottlieb maps by using derivation arguments in Sullivan models.
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