A rational obstruction to be a Gottlieb map

الأصل · EN

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.