Closed 1-Forms and Twisted Cohomology

30 Jun 2020 · Moroianu Andrei, Pilca Mihaela ·

We show that the first twisted cohomology group associated to closed 1-forms on compact 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.