✦ LIBER ✦
Homotopy classification of module bundles via Grassmannians
✍ Scribed by Maria H. Papatriantafillou
- Publisher
- John Wiley and Sons
- Year
- 2007
- Tongue
- English
- Weight
- 112 KB
- Volume
- 280
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
Abstract
Given a Waelbroeck ring R, we prove that the Grassmannian of a projective finitely generated R ‐module is a topological manifold modeled on a topological abelian group of R ‐linear maps. Fibre bundles of fibre type a module as above, over a compact base space B, admitting R ‐valued partitions of unity, are classified by the homotopy classes of continuous maps on B with values in the respective Grassmannian. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)