2017/05/17 by Saiei-Jaeyeong Matsubara-Heo, Matsubara-Heo, Saiei-Jaeyeong
Computer Science · Medicine · #Algebraic Geometry (math.AG) #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Medical Imaging Techniques and Applications #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1705.06052
openalex publication_date 2017/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In \citehien, M. Hien introduced rapid decay homology group \Homord*(U, (∇, E)) associated to an irregular connection (∇, E) on a smooth complex affine variety U, and showed that it is the dual group of the algebraic de Rham cohomology group \Homo^*dR(U,(∇\vee, E\vee)). On the other hand, F. Pham has already introduced his version of rapid decay homology when (∇, E) is the so-called elementary irregular connection (\citeSab) in \citePham. In this report, we will state a comparison theorem of these homology groups and give an outline of its proof. This can be regarded as a homological counterpart of the result \citeSab of C. Sabbah. As an application, we construct a basis of some rapid decay homologies associated to a hyperplane arrangement and hypersphere arrangement of Schlöfli type.