On the Morse–Novikov Cohomology of blowing up complex manifolds

Yongpan Zou

doi:10.5802/crmath.12

Géométrie algébrique, Géométrie différentielle

On the Morse–Novikov Cohomology of blowing up complex manifolds
[Sur la cohomologie de Morse-Novikov des éclatements de variétés complexes]

Yongpan Zou ¹

¹ School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China

Comptes Rendus. Mathématique, Volume 358 (2020) no. 1, pp. 67-77.

Résumé
Abstract

Inspiré par les récents travaux de S. Rao, S. Yang, X.-D. Yang et L. Meng sur les formules donnant le comportement des groupes de cohomologie de de Rham et Morse-Novikov dans les éclatements, nous donnons une nouvelle preuve simple de la formule pour la cohomologie de Morse-Novikov en introduisant le groupe de cohomologie de Morse-Novikov relatif via la cohomologie des faisceaux et en explicitant l’isomorphisme de la formule.

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.

Reçu le : 2019-08-03
Révisé le : 2019-11-25
Accepté le : 2019-12-16
Publié le : 2020-03-18

DOI : 10.5802/crmath.12

Affiliations des auteurs :

Yongpan Zou ¹

¹ School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {On the {Morse{\textendash}Novikov} {Cohomology} of blowing up complex manifolds},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {67--77},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {1},
     year = {2020},
     doi = {10.5802/crmath.12},
     language = {en},
}

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Yongpan Zou. On the Morse–Novikov Cohomology of blowing up complex manifolds. Comptes Rendus. Mathématique, Volume 358 (2020) no. 1, pp. 67-77. doi : 10.5802/crmath.12. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.12/

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