Homotopy classes of proper maps out of vector bundles

Thomas O. Rot*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

In this paper, we classify the homotopy classes of proper maps E→ Rk, where E is a vector bundle over a compact Hausdorff space. As a corollary, we compute the homotopy classes of proper maps Rn→ Rk. 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.

Original languageEnglish
Pages (from-to)107-117
Number of pages11
JournalArchiv der Mathematik
Volume114
Early online date30 Aug 2019
DOIs
Publication statusPublished - Jan 2020

Keywords

  • Framed cobordism
  • Pontryagin–Thom construction
  • Proper homotopy theory

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