Singularities of Mappings (original) (raw)

This work explores the singularities of mappings, particularly focusing on the conditions under which a point in a mapping is classified as regular or critical. It develops key invariants related to singularities from deformation theory and topology, emphasizing the differences in the geometrical singularity theories for mappings of varying dimensions. The implications of these invariants for understanding the local behavior of mappings are investigated, alongside discussions on codimension, normalizations, and relevant historical conjectures.