Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complements of connected hypersurfaces in $S^4$   We consider the possible Euler characteristics and fundamental groups of the
complementary components $X$ and $Y$ of an embedding of a connected closed
3-manifold $M$ in $S^4$. We use a 2-knot satellite construction to change the
fundamental groups, and Massey products to limit the values of $\chi(X)$ and
$\chi(Y)$ when $M$ is the total space of an $S^1$-bundle with orientable base
and Euler number 1.

12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an