Morse-Novikov cohomology on complex manifolds

DOI10.1007/S12220-019-00155-WzbMATH Open1436.32032arXiv1808.01057OpenAlexW2951437509WikidataQ128536316 ScholiaQ128536316MaRDI QIDQ2303801

Lingxu Meng

Publication date: 5 March 2020

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1808.01057

zbMATH Keywords

\( \eta \)-Hodge number\( \theta \)-Betti numberbimeromorphic invariantsDolbeault-Morse-Novikov cohomologysheaf of \(\eta \)-holomorphic functions

Mathematics Subject Classification ID

Analytic sheaves and cohomology groups (32C35) Algebraic topology on manifolds and differential topology (57R19)

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Related Items (7)

Morse-Novikov cohomology of locally conformally Kähler surfaces ⋮ Complexifications of Morse functions and the directed Donaldson-Fukaya category ⋮ Hypercohomologies of truncated twisted holomorphic de Rham complexes ⋮ Bott-Chern hypercohomology and bimeromorphic invariants ⋮ Leray-Hirsch theorem and blow-up formula for Dolbeault cohomology ⋮ The Witten deformation of the Dolbeault complex ⋮ On the Morse-Novikov cohomology of blowing up complex manifolds

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