Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bundles with non-multiplicative $\hat{A}$-genus and spaces of metrics
  with lower curvature bounds   We construct smooth bundles with base and fiber products of two spheres whose
total spaces have non-vanishing $\hat{A}$-genus. We then use these bundles to
locate non-trivial rational homotopy groups of spaces of Riemannian metrics
with lower curvature bounds for all Spin-manifolds of dimension six or at least
ten which admit such a metric and are a connected sum of some manifold and $S^n
\times S^n$ or $S^n \times S^{n+1}$, respectively. We also construct manifolds
$M$ whose spaces of Riemannian metrics of positive scalar curvature have
homotopy groups that contain elements of infinite order which lie in the image
of the orbit map induced by the push-forward action of the diffeomorphism group
of $M$.

14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat