Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Bound on the Cohomology of Quasiregularly Elliptic Manifolds   We show that a closed, connected and orientable Riemannian manifold of
dimension $d$ that admits a quasiregular mapping from $\mathbb R^d$ must have
bounded cohomological dimension independent of the distortion of the map. The
dimension of the degree $l$ de Rham cohomology of $M$ is bounded above by
$\binom{d}{l}$. This is a sharp upper bound that proves the Bonk-Heinonen
conjecture. A corollary of this theorem answers an open problem posed by Gromov
in 1981. He asked whether there exists a $d$-dimensional, simply connected
manifold that does not admit a quasiregular map from $\mathbb R^d$. Our result
gives an affirmative answer to this question.

9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph