Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the length of cohomology spheres   We present the length, a numerical cohomological index theory, of $ G
$-spaces which are cohomology spheres and $ G $ is a $p$-torus or a torus
group, where $p$ is a prime. As a consequence, we obtain Borsuk-Ulam and
Bourgin-Yang type theorems in this context. A sharper version of the
Bourgin-Yang theorem for topological manifolds is also proved. Also, we give
some general results regarding the upper and lower bound for the length.

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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
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The categories of this paper are: gr-qc