2018/09/02 by Takahiro Matsuyuki, Matsuyuki, Takahiro
Mathematics · Physics and Astronomy · #18G55 #55R10 #55R40 #57R20 #Algebra over a field #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Bundle #Characteristic class #Class (philosophy) #Computer science #Euler characteristic #FOS: Mathematics #Fiber #Fiber bundle #Genus #Geometry #Homotopy and Cohomology in Algebraic Topology #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Space (punctuation) #Surface (topology) #Vector bundle #math.AT #msc:18G55 #msc:55R10 #msc:55R40 #msc:57R20
paper · pdf · doi:10.48550/arxiv.1809.00363
24 pages
openalex publication_date 2018/09/02 · arxiv created 2019/05/29 · arxiv updated 2019/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider an obstruction-theoretical construction of characteristic classes of fiber bundles by simplicial method. We can get a certain obstruction class for a deformation of C_∞-algebra models of fibers and a characteristic map from the exterior algebra of a vector space of derivations. Applying this construction for a surface bundle, we obtain the Euler class of a sphere bundle and the Morita-Miller-Mumford classes of a bundle with positive genus fiber.