Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moduli space of metrics of nonnegative sectional or positive Ricci
  curvature on homotopy real projective spaces   We show that the moduli space of metrics of nonnegative sectional curvature
on every homotopy ${\mathbb {R}} P^5$ has infinitely many path components. We
also show that in each dimension $4k+1$ there are at least $2^{2k}$ homotopy
${\mathbb {R}} P^{4k+1}$s of pairwise distinct oriented diffeomorphism type for
which the moduli space of metrics of positive Ricci curvature has infinitely
many path components. Examples of closed manifolds with finite fundamental
group with these properties were known before only in dimensions $4k+3\geq 7$.

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The categories of this paper are: acc-phys
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess