Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positive scalar curvature on $\mathbf{Pin}^\pm$- and
  $\mathbf{Spin}^c$-manifolds   It is well-known that spin structures and Dirac operators play a crucial role
in the study of positive scalar curvature metrics (psc-metrics) on compact
manifolds. Here we consider a class of non-spin manifolds with "almost spin"
structure, namely those with spin$^c$ or pin$^\pm$-structures. It turns out
that in those cases (under natural assumptions on such a manifold $M$), the
index of a relevant Dirac operator completely controls existence of a
psc-metric which is $S^1$- or $C_2$-invariant near a "special submanifold" $B$
of $M$. This submanifold $B\subset M$ is dual to the complex (respectively,
real) line bundle $L$ which determines the spin$^c$ or pin$^\pm$ structure on
$M$. We also show that these manifold pairs $(M,B)$ can be interpreted as
"manifolds with fibered singularities" equipped with "well-adapted
psc-metrics". This survey is based on our recent work as well as on our joint
work with Paolo Piazza.

10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con