On the Morse--Novikov Cohomology of blowing up complex manifolds

2019/07/31 by Yongpan Zou, Zou, Yongpan
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1907.13336

openalex publication_date 2019/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Inspired by the recent works of S. Rao--S. Yang--X.-D. Yang and L. Meng on the blow-up formulae for de Rham and Morse--Novikov cohomology groups, we give a new simple proof of the blow-up formula for Morse--Novikov cohomology by introducing the relative Morse--Novikov cohomology group via sheaf cohomology theory and presenting the explicit isomorphism therein.

Citations

• Mayer-Vietoris systems and their applications
• Hodge cohomology on blow-ups along subvarieties

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