Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopy classes of proper maps out of vector bundles   In this paper we classify the homotopy classes of proper maps $E\rightarrow
\mathbb R^k$, where $E$ is a vector bundle over a compact Hausdorff space. As a
corollary we compute the homotopy classes of proper maps $\mathbb
R^n\rightarrow \mathbb R^k$. We find a stability range of such maps. We
conclude with some remarks on framed submanifolds of non-compact manifolds, the
relationship with proper homotopy classes of maps and the Pontryagin-Thom
construction.

8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph