2018/11/14 by Lingxu Meng, Meng, Lingxu
Mathematics · #14F25 #32C35 #53C56 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1811.10500
openalex publication_date 2018/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce notions such as cdp presheaf, cds precosheaf, Mayer-Vietoris system, and investigate their properties. As applications, we study cohomologies with values in local systems on smooth manifolds and Dolbeault cohomologies with values in locally free sheaves on complex manifolds, where the compactness is not necessary for both cases. In particular, we write out explicit blow-up formulas for these cohomologies. Moreover, we compare the blow-up formula given by Rao, S., Yang, S. and Yang, X.-D. with ours, and then deduce that their formula is still an isomorphism in the noncompact case.