Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Integration Formula for the Moment Maps of Circle Actions   The integration of the exponential of the square of the moment map of the
circle action is studied by a direct stationary phase computation and by
applying the Duistermaat-Heckman formula. Both methods yield two distinct
formulas expressing the integral in terms of contributions from the critical
set of the square of the moment map. The cohomological pairings on the
symplectic quotient, including its volume (which was known to be a piecewise
polynomial), are computed explicitly using the asymptotic behavior of the two
formulas.

1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom