Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On almost free torus actions and Horrocks conjecture   We construct a model for cohomology of a space $X$ equipped with a torus $T$
action, whose homotopy orbit space $X_{T}$ is formal. This model represents
Koszul complex of its equivariant cohomology. Studying homological properties
of modules over polynomial ring we derive new bounds on homological rank
(dimension of cohomology ring) of $X$ equipped with almost free torus action.
We give a proof of toral rank conjecture for spaces with formal quotient in the
case of torus dimension $\le5$.

4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con