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arXiv · 1808.08073

Homotopy classes of proper maps out of vector bundles

Thomas O. Rot
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Abstract

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.

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Thomas O. Rot. 2018-08-24. Homotopy classes of proper maps out of vector bundles. https://arxiv.org/abs/1808.08073

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