Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lagrangians, SO(3)-instantons and mixed equation   The mixed equation, defined as a combination of the anti-self-duality
equation in gauge theory and Cauchy-Riemann equation in symplectic geometry, is
studied. In particular, regularity and Fredholm properties are established for
the solutions of this equation, and it is shown that the moduli spaces of
solutions to the mixed equation satisfy a compactness property which combines
Uhlenbeck and Gormov compactness theorems. The results of this paper are used
in a sequel to study the Atiyah-Floer conjecture.

17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th