Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The topological quantization and the branch process of the
  (k-1)-dimensional topological defects   In the light of $\phi$-mapping method and topological current theory, the
topological structure and the topological quantization of arbitrary dimensional
topological defects are obtained under the condition that the Jacobian
$J(\phi/v) \neq 0$. When $J(\phi/v)=0$, it is shown that there exist the
crucial case of branch process. Based on the implicit function theorem and the
Taylor expansion, we detail the bifurcation of generalized topological current
and find different directions of the bifurcation. The arbitrary dimensional
topological defects are found splitting or merging at the degenerate point of
field function $\vec \phi$ but the total charge of the topological defects is
still unchanged.

6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math