Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The space of sections of a smooth function   Given a compact manifold $X$ with boundary and a submersion $f : X
\rightarrow Y$ whose restriction to the boundary of $X$ has isolated critical
points with distinct critical values and where $Y$ is $[0,1]$ or $S^1$, the
connected components of the space of sections of $f$ are computed from $\pi_0$
and $\pi_1$ of the fibers of $f$. This computation is then leveraged to provide
new results on a smoothed version of the evasion path problem for mobile sensor
networks: From the time-varying homology of the covered region and the
time-varying cup-product on cohomology of the boundary, a necessary and
sufficient condition for existence of an evasion path and a lower bound on the
number of homotopy classes of evasion paths are computed. No connectivity
assumptions are required.

25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph