Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A homotopy decomposition of the fibre of the squaring map on
  $\Omega^3S^{17}$   We use Richter's $2$-primary proof of Gray's conjecture to give a homotopy
decomposition of the fibre $\Omega^3S^{17}\{2\}$ of the $H$-space squaring map
on the triple loop space of the $17$-sphere. This induces a splitting of the
mod-$2$ homotopy groups $\pi_\ast(S^{17}; \mathbb{Z}/2\mathbb{Z})$ in terms of
the integral homotopy groups of the fibre of the double suspension
$E^2:S^{2n-1} \to \Omega^2S^{2n+1}$ and refines a result of Cohen and Selick,
who gave similar decompositions for $S^5$ and $S^9$. We relate these
decompositions to various Whitehead products in the homotopy groups of mod-$2$
Moore spaces and Stiefel manifolds to show that the Whitehead square $[i_{2n},
i_{2n}]$ of the inclusion of the bottom cell of the Moore space $P^{2n+1}(2)$
is divisible by $2$ if and only if $2n=2, 4, 8$ or $16$.

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The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
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The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
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The categories of this paper are: eess