Morse-Novikov Cohomology Of Blowing Up Complex Manifolds And The Deformation Of CR-Structure

This paper is divided into two parts.In the first part we study the Morse-Novikov cohomology of blowing up complex manifolds.The second part is concerns about the deformation of CR-structure.For a complex manifold X and a submanifold Z ? X,the blow-up (?) of X along Z is a new complex manifold.We will study the relations between the Morse-Novikov cohomologies of (?) with those of X and Z.The Morse-Novikov cohomology here is a generalisation of de Rham cohomology.It is a celebrated result in deformation theory that the deformations of CalabiYau manifolds are unobstructed,by the Bogomolov-Tian-Todorov theorem.For the deformation of CR-structures,T.Akahori-K.Miyajima obtained the unobstructedness for deformations of CR structures.In this paper,we reprove this main theorem by the power series methods.This thesis is divided into 3 chapters:In Chapter One we introduce some basic concepts and research background.In Chapter Two we study the Morse-Novikov cohomology of blowing up complex manifolds.Firstly we give some preliminaries on sheaf theory.Then we proved the blow-up formula by the relative cohomology methods originally from [30].In Chapter Three we study the deformation of CR-structure.Firstly we introduce some necessary preliminaries,then we establish the crucial lemma 3.3.1 with proof.Finally according to this lemma we reprove the main theorem.