Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Splitting off Rational Parts in Homotopy Types   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.

11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol