Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Yang-Mills theory over surfaces and the Atiyah-Segal theorem   In this paper we explain how Morse theory for the Yang-Mills functional can
be used to prove an analogue, for surface groups, of the Atiyah-Segal theorem.
Classically, the Atiyah-Segal theorem relates the representation ring R(\Gamma)
of a compact Lie group $\Gamma$ to the complex K-theory of the classifying
space $B\Gamma$. For infinite discrete groups, it is necessary to take into
account deformations of representations, and with this in mind we replace the
representation ring by Carlsson's deformation $K$--theory spectrum $\K
(\Gamma)$ (the homotopy-theoretical analogue of $R(\Gamma)$). Our main theorem
provides an isomorphism in homotopy $\K_*(\pi_1 \Sigma)\isom K^{-*}(\Sigma)$
for all compact, aspherical surfaces $\Sigma$ and all $*>0$. Combining this
result with work of Tyler Lawson, we obtain homotopy theoretical information
about the stable moduli space of flat unitary connections over surfaces.

16
The categories of this paper are: stat
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph