Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Removing parametrized rays symplectically   Extracting isolated rays from a symplectic manifold result in a manifold
symplectomorphic to the initial one. The same holds for higher dimensional
parametrized rays under an additional condition. More precisely, let
$(M,\omega)$ be a symplectic manifold. Let $[0,\infty)\times
Q\subset\mathbb{R}\times Q$ be considered as parametrized rays $[0,\infty)$ and
let $\varphi:[-1,\infty)\times Q\to M$ be an injective, proper, continuous map
immersive on $(-1,\infty)\times Q$. If for the standard vector field
$\frac{\partial}{\partial t}$ on $\mathbb{R}$ and any further vector field
$\nu$ tangent to $(-1,\infty)\times Q$ the equation
$\varphi^*\omega(\frac{\partial}{\partial t},\nu)=0$ holds then $M$ and
$M\setminus \varphi([0,\infty)\times Q)$ are symplectomorphic.

5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs