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Mathematics > Differential Geometry

arXiv:1808.01057 (math)
[Submitted on 3 Aug 2018 (v1), last revised 2 Feb 2020 (this version, v4)]

Title:Morse-Novikov cohomology on complex manifolds

Authors:Lingxu Meng
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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.
Comments: 16 page, Theorem 4.6 and 4.9 were added
Subjects: Differential Geometry (math.DG); Complex Variables (math.CV)
MSC classes: 32C35, 57R19
Cite as: arXiv:1808.01057 [math.DG]
  (or arXiv:1808.01057v4 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.1808.01057
Journal reference: J. Geom. Anal. 30 (2020), no. 1, 493-510
Related DOI: https://doi.org/10.1007/s12220-019-00155-w

Submission history

From: Lingxu Meng [view email]
[v1] Fri, 3 Aug 2018 01:11:18 UTC (13 KB)
[v2] Wed, 31 Oct 2018 15:54:47 UTC (14 KB)
[v3] Wed, 16 Jan 2019 03:02:30 UTC (16 KB)
[v4] Sun, 2 Feb 2020 01:01:14 UTC (16 KB)
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