Closed 1-Forms and Twisted Cohomology
arXiv:2003.10368 · doi:10.1007/s12220-020-00595-9
Abstract
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.
13 pages, a gap in the proof of Lemma 1.1 corrected