Splitting off Rational Parts in Homotopy Types

Details Splitting off Rational Parts in Homotopy Types Splitting off Rational Parts in Homotopy Types

2004-11-16

arxiv.org/abs/math/0411360v1

Mathematics

Algebraic Topology

6 pages

Scientific paper

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 $\bar{\rho} : [S_{\Q}^{n},X] \to H_n(X;\Z)$ 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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