Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gauge theoretical equivariant Gromov-Witten invariants and the full
  Seiberg-Witten invariants of ruled surfaces   Let $(F,J,\omega)$ be an almost K\"ahler manifold, $\alpha$ a $J$-holomorphic
action of a compact Lie group $\hat K$ on $F$, and $K$ a closed normal subgroup
of $\hat K$ which leaves $\omega$ invariant. We introduce gauge theoretical
invariants for such triples $(F,\alpha,K)$. The invariants are associated with
moduli spaces of solutions of a certain vortex type equation on a Riemann
surface.
  We give explicite descriptions of the moduli spaces associated with the
triple $(\Hom(\C^r,\C^{r_0}), \alpha_{\rm can},U(r))$, where $\alpha_{\rm can}$
denotes the canonical action of $\hat K=U(r)\times U(r_0)$ on
$\Hom(\C^r,\C^{r_0})$. In the abelian case $r=1$, the new invariants can be
computed expliciteley and identified with the full Seiberg-Witten invariants of
ruled surfaces.

26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
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The categories of this paper are: adap-org