Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the cohomology of the free loop space of a complex projective space   Let $\Lambda (\mathbb{C}P^n)$ denote the free loop space of the complex
projective space $\mathbb{C}P^n$, i. e. $\mathbb{C}P^n$ is the projective space
of the vector space $\mathbb{C}^{n+1}$ of dimension $n+1$ over the complex
numbers $\mathbb{C}$ and $\Lambda(\mathbb{C}P^n)$ is the function space
$\mathrm{map}(S^1,\mathbb{C}P^n)$ of unbased maps from a circle $S^1$ into
$\mathbb{C}P^n$ topologized with the compact open topology. In this note we
show that despite the fact that the natural fibration
$\Omega(\mathbb{C}P^n)\hookrightarrow
\Lambda(\mathbb{C}P^n)\stackrel{eval}{\longrightarrow}\mathbb{C}P^n$ has a
cross section its Serre spectral sequence does not collapse: Here $eval$ is the
evaluation map at a base point * $\in \mathbb{C}P^n$.

12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga