Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Foliations and Global Inversion   We consider topological conditions under which a locally invertible map
admits a global inverse. Our main theorem states that a local diffeomorphism
$f: M \to\mathbb{R}^n$ is bijective if and only if $H_{n-1}(M)=0$ and the
pre-image of every affine hyperplane is non-empty and acyclic. The proof is
based on some geometric constructions involving foliations and tools from
intersection theory. This topological result generalizes in finite dimensions
the classical analytic theorem of Hadamard-Plastock, including its recent
improvement by Nollet-Xavier. The main theorem also relates to a conjecture of
the aforementioned authors, involving the well known Jacobian Conjecture in
algebraic geometry.

20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci