Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Cohomology of the Classifying Spaces of Projective Unitary Groups   Let $\mathbf{B}PU_{n}$ be the classifying space of $PU_n$, the projective
unitary group of order $n$, for $n>1$. We use the Serre spectral sequence
associated to a fiber sequence
$\mathbf{B}U_n\rightarrow\mathbf{B}PU_n\rightarrow K(\mathbb{Z},3)$ to
determine the ring structure of $H^{*}(\mathbf{B}PU_{n}; \mathbb{Z})$ up to
degree $10$, as well as a family of distinguished elements of
$H^{2p+2}(\mathbf{B}PU_{n}; \mathbb{Z})$, for each prime divisor $p$ of $n$. We
also study the primitive elements of $H^*(\mathbf{B}U_n;\mathbb{Z})$ as a
comodule over $H^*(K(\mathbb{Z},2);\mathbb{Z})$, where the comodule structure
is given by an action of $K(\mathbb{Z},2)\simeq\mathbf{B}S^1$ on $BU_n$
corresponding to the action of taking the tensor product of a complex line
bundle and an $n$ dimensional complex vector bundle.

29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph