Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An $HP^2$-bundle over $S^4$ with nontrivial $\hat{A}$-genus   We explain the existence of a smooth $HP^2$-bundle over $S^4$ whose total
space has nontrivial $\hat{A}$-genus. Combined with an argument going back to
Hitchin, this answers a question of Schick and implies that the space of
Riemannian metrics of positive sectional curvature on a closed manifold can
have nontrivial higher rational homotopy groups.

31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph