Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chern Rank of Complex Bundle   We introduce notions of {\it upper chernrank} and {\it even cup length} of a
finite connected CW-complex and prove that {\it upper chernrank} is a homotopy
invariant. It turns out that determination of {\it upper chernrank} of a space
$X$ sometimes helps to detect whether a generator of the top cohomology group
can be realized as Euler class for some real (orientable) vector bundle over
$X$ or not. For a closed connected $d$-dimensional complex manifold we obtain
an upper bound of its even cup length. For a finite connected even dimensional
CW-complex with its {\it upper chernrank} equal to its dimension, we provide a
method of computing its even cup length. Finally, we compute {\it upper
chernrank} of many interesting spaces.

9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph