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Homotopy classification of module bundles via Grassmannians
Author(s) -
Papatriantafillou Maria H.
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410473
Subject(s) - mathematics , grassmannian , pure mathematics , homotopy , homotopy group , vector bundle , abelian group , manifold (fluid mechanics) , topology (electrical circuits) , base (topology) , combinatorics , mathematical analysis , mechanical engineering , engineering
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)
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