2017/08/19 by Bikram Banerjee, Banerjee, Bikram
Computer Science · Mathematics · #57R20 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #msc:57R20
paper · pdf · doi:10.48550/arxiv.1708.05871
openalex publication_date 2017/08/19 · arxiv created 2018/01/23 · arxiv updated 2018/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce notions of \it upper chernrank and \it even cup length of a finite connected CW-complex and prove that \it upper chernrank is a homotopy invariant. It turns out that determination of \it upper chernrank of a space X sometimes helps to detect whether a generator of the top cohomology group can be realized as Euler class for some real (orientable) vector bundle over X or not. For a closed connected d-dimensional complex manifold we obtain an upper bound of its even cup length. For a finite connected even dimensional CW-complex with its \it upper chernrank equal to its dimension, we provide a method of computing its even cup length. Finally, we compute \it upper chernrank of many interesting spaces.