Splitting off Rational Parts in Homotopy Types

Norio Iwase; Nobuyuki Oda

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Splitting off Rational Parts in Homotopy Types

Norio Iwase·Nobuyuki Oda

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Abstract

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 \cite{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 $\barρ : [S_{\Q}^{n},X] \to H_n(X;\Z)$ 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.

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BibTeX RIS

Norio Iwase, Nobuyuki Oda. 2004-11-16. Splitting off Rational Parts in Homotopy Types. https://arxiv.org/abs/math/0411360

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