Year: 2018
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Meng, Lingxu
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2901616402