Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Borsuk-Ulam theorem for $(\mathbb Z_p)^k$-actions on products of (mod
  $p$) homology spheres   It is proved that for a product action of $(\mathbb Z_p)^k$ on a product of
(mod p) homology spheres $N^{n_1}\times...\times N^{n_k}$, where all $n_i$'s
are assumed to be odd if $p$ is odd, and any continuous map $f\colon
N^{n_1}\times...\times N^{n_k}\to \mathbb R^m$ the set $A(f)=\{x\in
N^{n_1}\times...\times N^{n_k}| f(x)=f(gx) \forall g\in(\mathbb Z_p)^k\}$ has
dimension at least $n_1+...+n_k-m(p^k-1)$, provided $n_i\ge mp^{i-1}(p-1)$ for
all $i (1\le i\le k)$. Moreover, if $n_i\ge mp^{k-1}(p-1)$ for all $i(1\le i\le
k)$ then the free action $\mu$ can be assumed arbitrary.

11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex