Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The braid groups of the projective plane and the Fadell-Neuwirth short
  exact sequence   We study the pure braid groups $P_n(RP^2)$ of the real projective plane
$RP^2$, and in particular the possible splitting of the Fadell-Neuwirth short
exact sequence $1 \to P_m(RP^2 {x_1,...,x_n} \to P_{n+m}(RP^2)
\stackrel{p_{\ast}}{\to} P_n(RP^2) \to 1$, where $n\geq 2$ and $m\geq 1$, and
$p_{\ast}$ is the homomorphism which corresponds geometrically to forgetting
the last $m$ strings. This problem is equivalent to that of the existence of a
section for the associated fibration $p: F_{n+m}(RP^2) \to F_n(RP^2)$ of
configuration spaces. Van Buskirk proved in 1966 that $p$ and $p_{\ast}$ admit
a section if $n=2$ and $m=1$. Our main result in this paper is to prove that
there is no section if $n\geq 3$. As a corollary, it follows that $n=2$ and
$m=1$ are the only values for which a section exists. As part of the proof, we
derive a presentation of $P_n(RP^2)$: this appears to be the first time that
such a presentation has been given in the literature.

17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an