Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal moduli spaces of surfaces with flat connections and cobordism
  theory   Given a semisimple, compact, connected Lie group G with complexification G^c,
we show there is a stable range in the homotopy type of the universal moduli
space of flat connections on a principal G-bundle on a closed Riemann surface,
and equivalently, the universal moduli space of semistable holomorphic
G^c-bundles. The stable range depends on the genus of the surface. We then
identify the homology of this moduli space in the stable range in terms of the
homology of an explicit infinite loop space. Rationally this says that the
stable cohomology of this moduli space is generated by the
Mumford-Morita-Miller kappa-classes, and the ring of characteristic classes of
principal G-bundles, H^*(BG). We then identify the homotopy type of the
category of one-manifolds and surface cobordisms, each equipped with a flat
G-bundle. We also explain how these results may be generalized to arbitrary
compact connected Lie groups. Our methods combine the classical techniques of
Atiyah and Bott, with the new techniques coming out of Madsen and Weiss's proof
of Mumford's conjecture on the stable cohomology of the moduli space of Riemann
surfaces.

11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an