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Morse-Novikov cohomology on complex manifolds (1808.01057v4)
Published 3 Aug 2018 in math.DG and math.CV
Abstract: We view Dolbeault-Morse-Novikov cohomology H{p,q}_\eta(X) as the cohomology of the sheaf \Omega_{X,\eta}p of \eta-holomorphic p-forms and give several bimeromorphic invariants. Analogue to Dolbeault cohomology, we establish the Leray-Hirsch theorem and the blow-up formula for Dolbeault-Morse-Novikov cohomology. At last, we consider the relations between Morse-Novikov cohomology and Dolbeault-Morse-Novikov cohomology, moreover, investigate stabilities of their dimensions under the deformations of complex structures. In some aspects, Morse-Novikov and Dolbeault-Morse-Novikov cohomology behave similarly with de Rham and Dolbeault cohomology.