11 citations · 48 across the 15 of their papers we have counts for
5 papers · 1 filter
Mayer-Vietoris systems and their applications
Lingxu Meng
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 syst…
Complex Balanced Spaces
Jixiang Fu, Lingxu Meng, Wei Xia
In this paper, the concept of balanced manifolds is generalized to reduced complex spaces: the class B and balanced spaces. Compared with the case of Kahlerian, the class B is simi…
Morse-Novikov cohomology on complex manifolds
Lingxu Meng
We view Dolbeault-Morse-Novikov cohomology H^{p,q}_η(X) as the cohomology of the sheaf Ω_{X,η}^p of η-holomorphic p-forms and give several bimeromorphic invariants. Analogue to Dol…
Leray-Hirsch theorem and blow-up formula for Dolbeault cohomology
Lingxu Meng
We prove a theorem of Leray-Hirsch type and give an explicit blow-up formula for Dolbeault cohomology on (\emph{not necessarily compact}) complex manifolds. We give applications to…
Morse-Novikov cohomology for blow-ups of complex manifolds
Lingxu Meng
The weight -sheaf helps us to reinterpret Morse-Novikov cohomologies via sheaf theory. We give several theorems of Künneth and Leray-Hirsch types.…