Splitting off Rational Parts in Homotopy Types

Original · EN

It is known algebraically that any abelian group is a direct sum of a divisible group and a reduced group (See Theorem 21.3 of Fuchs:abelian-group). In this paper, conditions to split off rational parts in homotopy types from a given space are studied in terms of a variant of Hurewicz map, say ρ: [Sⁿ,X] → Hₙ(X;) and generalized Gottlieb groups. This yields decomposition theorems on rational homotopy types of Hopf spaces, T-spaces and Gottlieb spaces, which has been known in various situations, especially for spaces with finiteness conditions.