Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sobolev mappings, degree, homotopy classes and rational homology spheres   In the paper we investigate the degree and the homotopy theory of
Orlicz-Sobolev mappings $W^{1,P}(M,N)$ between manifolds, where the Young
function $P$ satisfies a divergence condition and forms a slightly larger space
than $W^{1,n}$, $n=\dim M$. In particular, we prove that if $M$ and $N$ are
compact oriented manifolds without boundary and $\dim M=\dim N=n$, then the
degree is well defined in $W^{1,P}(M,N)$ if and only if the universal cover of
$N$ is not a rational homology sphere, and in the case $n=4$, if and only if
$N$ is not homeomorphic to $S^4$.

33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an