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Morse-Novikov Cohomology on Complex Manifolds

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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.

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Acknowledgements

I would like to express my gratitude to referees for their helpful suggestions and careful reading of my manuscript.

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  1. Department of Mathematics, North University of China, Taiyuan, Shanxi, 030051, People’s Republic of China

    Lingxu Meng

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  1. Lingxu Meng
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Correspondence to Lingxu Meng.

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Meng, L. Morse-Novikov Cohomology on Complex Manifolds. J Geom Anal 30, 493–510 (2020). https://doi.org/10.1007/s12220-019-00155-w

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