The size of some vanishing and critical sets - PINTEA, Cornel (Studia Universitatis Babeș-Bolyai Mathematica, 2020)
We prove that the vanishing sets of all top forms on a non-orientable manifold are at least 1-dimensional in the general case and at most 1-codimensional in the compact case. We apply these facts to show that the critical sets of some differentiable maps are at least 1-dimensional in the general case and at most 1-codimensional when the source manifold is compact. Mathematics Subject Classification (2010): 57R70, 57R35, 57M10.