Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Localization and Stationary Phase Approximation on Supermanifolds   Given an odd vector field $Q$ on a supermanifold $M$ and a $Q$-invariant
density $\mu$ on $M$, under certain compactness conditions on $Q$, the value of
the integral $\int_{M}\mu$ is determined by the value of $\mu$ on any
neighborhood of the vanishing locus $N$ of $Q$. We present a formula for the
integral in the case where $N$ is a subsupermanifold which is appropriately
non-degenerate with respect to $Q$.
  In the process, we discuss the linear algebra necessary to express our result
in a coordinate independent way. We also extend stationary phase approximation
and the Morse-Bott Lemma to supermanifolds.

0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat