2010/09/30 by Igor Nikolaev
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Covariant transformation #Dimension (graph theory) #Exact functor #Functor #Homotopy and Cohomology in Algebraic Topology #Topology (electrical circuits) #Torus #math.AT #math.OA #msc:46L85 #msc:55S35
paper · pdf · doi:10.1007/s10587-015-0228-8
published in Czechoslovak Mathematical Journal 65(4), 1069-1083 (Springer Nature) · to appear Czechoslovak Math. J
arxiv created 2015/03/04 · openalex publication_date 2015/12/01 · arxiv updated 2016/01/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The paper studies applications of C *-algebras in geometric topology. Namely, a covariant functor from the category of mapping tori to a category of AF -algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding AF -algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension 2, 3 and 4. In conclusion, we consider two numerical examples illustrating our main results.