Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Any finite group acts freely and homologically trivially on a product of
  spheres   The main theorem is that if K is a finite CW complex with finite fundamental
group G and universal cover homotopy equivalent to a product of spheres X, then
G acts smoothly and freely on X x S^n for any n greater than or equal to the
dimension of X. If the G-action on the universal cover of K is homologically
trivial then so is the action on X x S^n.
  Unlu and Yalcin recently showed that for every finite group G, there is a
finite CW complex K with fundamental group G which acts homologicially
trivially on the universal cover of K.
  Thus every finite group acts smoothly, freely, and homologically trivially on
a product of spheres.

20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin