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

TL;DR

This paper provides a new, simplified proof of the blow-up formula for Morse--Novikov cohomology of complex manifolds, using sheaf cohomology and relative cohomology groups.

Contribution

It introduces a novel approach to the blow-up formula for Morse--Novikov cohomology through sheaf cohomology and explicit isomorphisms, simplifying previous proofs.

Findings

New proof of blow-up formula for Morse--Novikov cohomology

Introduction of relative Morse--Novikov cohomology group

Explicit isomorphism construction

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.