Morse-Novikov cohomology for blow-ups of complex manifolds (Q2685167)

The paper is dedicated to the study of Morse-Novikov cohomology for blow-ups of complex manifolds through weight \(\theta\)-sheaf \(\underline{\mathbb{R}}_{X,\theta}\). The author gives the elementary properties of weight \(\theta\)-sheaf \(\underline{\mathbb{R}}_{X,\theta}\) and also establishes several theorems of Künneth and Leray-Hirsch types. Then the computation of Morse-Novikov cohomologies of projective bundles as well as the independence between \(\theta\)-Lefschetz number and \(\theta\) are given. Finally blow-up formulae on complex manifolds is investigated.