Splitting off rational parts in homotopy types

Norio Iwase, Nobuyuki Oda

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 [L. Fuchs, Infinite Abelian Groups, vol. I, Academic Press, New York-London, 1970]). 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 ρ̄ : [Sn, X] → Hn ℤ) and generalised 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.

Original languageEnglish
Pages (from-to)133-140
Number of pages8
JournalTopology and its Applications
Volume153
Issue number1
DOIs
Publication statusPublished - Aug 1 2005

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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