Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An algebraic formula for the index of a 1-form on a real quotient
  singularity   Let a finite abelian group $G$ act (linearly) on the space $\mathbb{R}^n$ and
thus on its complexification $\mathbb{C}^n$. Let $W$ be the real part of the
quotient $\mathbb{C}^n/G$ (in general $W \neq \mathbb{R}^n/G$). We give an
algebraic formula for the radial index of a 1-form on the real quotient $W$. It
is shown that this index is equal to the signature of the restriction of the
residue pairing to the $G$-invariant part $\Omega^G_\omega$ of $\Omega_\omega=
\Omega^n_{\mathbb{R}^n,0}/\omega \wedge \Omega^{n-1}_{\mathbb{R}^n,0}$. For a
$G$-invariant function $f$, one has the so-called quantum cohomology group
defined in the quantum singularity theory (FJRW-theory). We show that, for a
real function $f$, the signature of the residue pairing on the real part of the
quantum cohomology group is equal to the orbifold index of the 1-form $df$ on
the preimage $\pi^{-1}(W)$ of $W$ under the natural quotient map.

4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th