Homotopy classes of proper maps out of vector bundles

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
Issue number1
Early online date30 Aug 2019
DOIs
Publication statusPublished - 1 Jan 2020

Fingerprint

Proper Map
Vector Bundle
Homotopy
Noncompact Manifold
Compact Hausdorff Space
Submanifolds
Corollary
Classify
Range of data
Class

Keywords

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

Cite this

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Homotopy classes of proper maps out of vector bundles. / Rot, Thomas O.

In: Archiv der Mathematik, Vol. 114, No. 1, 01.01.2020, p. 107-117.

Research output: Contribution to JournalArticleAcademicpeer-review

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