Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological classification of complex vector bundles over
  $8$-dimensional spin$^{c}$ manifolds   In this paper, complex vector bundles of rank $r$ over $8$-dimensional
spin$^{c}$ manifolds are classified in terms of the Chern classes of the
complex vector bundles and the cohomology ring of the manifolds, where $r = 3$
or $4$. As an application, we got that two rank $3$ complex vector bundles over
$4$-dimensional complex projective spaces $\C P^{4}$ are isomorphic if and only
if they have the same Chern classes. Moreover, the Chern classes of rank $3$
complex vector bundles over $\C P^{4}$ are determined. Combing Thomas's and
Switzer's results with our work, we can assert that complex vector bundles over
$\C P^{4}$ are all classified.

36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org