Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopy type of spaces of curves with constrained curvature on flat
  surfaces   Let $S$ be a complete flat surface, such as the Euclidean plane. We determine
the homeomorphism class of the space of all curves on $S$ which start and end
at given points in given directions and whose curvatures are constrained to lie
in a given open interval, in terms of all parameters involved. Any connected
component of such a space is either contractible or homotopy equivalent to an
$n$-sphere, and every $n\geq 1$ is realizable. Explicit homotopy equivalences
between the components and the corresponding spheres are constructed.

1
The categories of this paper are: cs
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex