Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite group actions on homology spheres and manifolds with nonzero
  Euler characteristic   Let $X$ be a smooth manifold belonging to one of these three collections:
acyclic manifolds (compact or not, possibly with boundary), compact connected
manifolds (possibly with boundary) with nonzero Euler characteristic, integral
homology spheres. We prove that $Diff(X)$ is Jordan. This means that there
exists a constant $C$ such that any finite subgroup $G$ of $Diff(X)$ has an
abelian subgroup whose index in $G$ is at most $C$. Using a result of Randall
and Petrie we deduce that the automorphism groups of connected, non necessarily
compact, smooth real affine varieties with nonzero Euler characteristic are
Jordan.

1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin