Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponents of $[\Omega(\mathbb S^{r+1}), \Omega (Y)]$   We investigate the exponents of the total Cohen groups $[\Omega(\mathbb
S^{r+1}), \Omega(Y)]$ for any $r\ge 1$. In particular, we show that for $p\ge
3$, the $p$-primary exponents of $[\Omega(\mathbb S^{r+1}), \Omega(\mathbb
S^{2n+1})]$ and $[\Omega(\mathbb S^{r+1}), \Omega(\mathbb S^{2n})]$ coincide
with the $p$-primary homotopy exponents of spheres $\mathbb S^{2n+1}$ and
$\mathbb S^{2n}$, respectively.
  We further study the exponent problem when $Y$ is a space with the homotopy
type of $\Sigma(n)/G$ for a homotopy $n$-sphere $\Sigma(n)$, the complex
projective space $\mathbb{C}P^n$ for $n\ge 1$ or the quaternionic projective
space $\mathbb{H}P^n$ for $1\le n\le \infty$.

36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int