The size of some vanishing and critical sets
DOI:
https://doi.org/10.24193/subbmath.2020.4.11Keywords:
Critical and vanishing sets.Abstract
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.
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