2001/04/06 by Igor Nikolaev, Nikolaev, Igor
Mathematics · #19K35 #46L40 #58F10 #Abelian group #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Mathematics #Pure mathematics #Rings, Modules, and Algebras #math.DG #math.KT #msc:19K35 #msc:46L40 #msc:58F10
paper · pdf · doi:10.48550/arxiv.math/0104085
arxiv created 2001/04/06 · openalex publication_date 2001/04/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
If X is a CW complex, one can assign to each point of X an ordered abelian group of finite rank whose subset of positive elements depends continuously on the points of X. A locally trivial bundle which arises in this way we denote by E(X). In the present work we establish a topological classification of such bundles in terms of the first cohomology group of X with coefficients in the ring Z2. This result has an amazing application in the theory of characteristic classes of foliations on compact manifolds.