Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Borsuk-Ulam property for homotopy classes of maps between the torus
  and the Klein bottle   Let $M$ be a topological space that admits a free involution $\tau$, and let
$N$ be a topological space. A homotopy class $\beta \in [ M,N ]$ is said to
have {\it the Borsuk-Ulam property with respect to $\tau$} if for every
representative map $f: M \to N$ of $\beta$, there exists a point $x \in M$ such
that $f(\tau(x))= f(x)$. In this paper, we determine the homotopy classes of
maps from the $2$-torus $T^2$ to the Klein bottle $K^2$ that possess the
Borsuk-Ulam property with respect to a free involution $\tau_1$ of $T^2$ for
which the orbit space is $T^2$. Our results are given in terms of a certain
family of homomorphisms involving the fundamental groups of $T^2$ and $K^2$.

23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th