TY - JOUR
T1 - Splitting off rational parts in homotopy types
AU - Iwase, Norio
AU - Oda, Nobuyuki
N1 - Funding Information:
* Corresponding author. E-mail addresses: iwase@math.kyushu-u.ac.jp (N. Iwase), odanobu@cis.fukuoka-u.ac.jp (N. Oda). 1 The author is supported by the Grant-in-Aids for Scientific Research #14654016 from the Ministry of Education, Culture, Sports, Science and Technology, Japan. 2 The author is supported by the Grant-in-Aids for Scientific Research #15340025 from the Japan Society for the Promotion of Science.
PY - 2005/8/1
Y1 - 2005/8/1
N2 - 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 : [Sℚn, 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.
AB - 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 : [Sℚn, 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.
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U2 - 10.1016/j.topol.2005.01.027
DO - 10.1016/j.topol.2005.01.027
M3 - Article
AN - SCOPUS:25444460230
SN - 0166-8641
VL - 153
SP - 133
EP - 140
JO - Topology and its Applications
JF - Topology and its Applications
IS - 1
ER -