Abstract
Inspiré par les récents travaux de S. Rao, S. Yang, X.-D. Yang et L. Meng sur les formules donnant le comportement des groupes de cohomologie de de Rham et Morse-Novikov dans les éclatements, nous donnons une nouvelle preuve simple de la formule pour la cohomologie de Morse-Novikov en introduisant le groupe de cohomologie de Morse-Novikov relatif via la cohomologie des faisceaux et en explicitant l’isomorphisme de la formule.
Highlights
Let X be a smooth manifold and A p (X ) the space of smooth p-forms on X
/ ···, whose cohomology Hθp (X ) := H p (A (X ), dθ) is called p-th Morse–Novikov cohomology group. This cohomology was originally defined by Lichnerowicz [4, 7] and Novikov [10] in the context of Poisson geometry and Hamiltonian mechanics, respectively
One significant application of locally conformally Kählerian structure in complex geometry is the classification of compact non-Kähler complex surfaces
Summary
Let X be a smooth manifold and A p (X ) the space of smooth p-forms on X. Zhao prove a blow-up formula of Morse–Novikov cohomology for compact locally conformal Kähler manifolds with the submanifold Z ⊆ X is a compact induced globally conformal Kähler submanifold, that is, the restriction of the Lee form θ|Z is exact. Meng systematically studies the behavior of Morse–Novikov cohomology under blow-up along a connected complex submanifold Z. He uses many topological tools such as Mayer–Vietoris sequences. We mainly use the relative cohomological method in [12, 13, 14] and the sheaf theory from [8] as in Subsection 2.3 for the crucial Proposition 6 to give a new simple proof of the blow-up formula for Morse–Novikov cohomology with an explicit isomorphism: Main Theorem 1. We are not able to apply the relative cohomological method via the compactly supported cohomology directly as [12, 13]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
