Cobordism groups of immersions of oriented manifolds
This paper is a calculation of the cobordism group of immersions of oriented manifolds in Euclidean spaces. The approach taken is to compose the immersion with the projection of Euclidean space on a hyperplane. This idea was used by T. Banchoff and U. Koschorke who study the immersion by analyzing the singular set of the composition. The new feature here is to construct a classifying space for the cobordism of these singular maps. Using a filtration of the classifying space with simple quotient spaces, Koschorke's exact sequences arise as the homotopy exact sequences for pairs. Here the spectral sequence of the filtration is used to get results in a wider range.
cobordism group of immersions of oriented manifolds in Euclidean spaces
scientific article; zbMATH DE number 556327
scientific article