Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Embedded curves and Gromov-Witten invariants of three-folds   Associated with a prime homology class $\beta \in P_2(X,\Z)$ (i.e.
$\beta=p\alpha$ and $\alpha \in H_2(X,\Z)$ imply $p=1$ or $p$ is an odd prime)
on a symplectic three-manifold with vanishing first Chern class, we count the
embedded perturbed pseudo-holomorphic curves in $X$ of a fixed genus $g$ to
obtain certain integer valued invariants analogous to Gromov-Witten invariants
of $X$.

24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph