Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Epimorphisms of 3-manifold groups   Let $f\colon M\to N$ be a proper map between two aspherical compact
orientable 3-manifolds with empty or toroidal boundary. We assume that $N$ is
not a closed graph-manifold. Suppose that $f$ induces an epimorphism on
fundamental groups. We show that $f$ is homotopic to a homeomorphism if one of
the following holds: either for any finite-index subgroup $\Gamma$ of
$\pi_1(N)$ the ranks of $\Gamma$ and of $f_*^{-1}(\Gamma)$ agree, or for any
finite cover $\tilde{N}$ of $N$ the Heegaard genus of $\tilde{N}$ and the
Heegaard genus of the pull-back cover $\tilde{M}$ agree.

26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph