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Closed 1-Forms and Twisted Cohomology

Andrei Moroianu,Mihaela Pilca

The Journal of Geometric Analysis（2021）

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Abstract
We show that the first twisted cohomology group associated with closed 1-forms on differentiable manifolds is related to certain 2-dimensional representations of the fundamental group. In particular, we construct examples of nowhere-vanishing 1-forms with non-trivial twisted cohomology.
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Twisted cohomology, Morse-Novikov cohomology, Vaisman manifolds, Cohomology group, Closed 1-form, Group representation, Fundamental group, 53A30, 53B35, 53C25, 53C29, 53C55
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