Generalization of the Whitney-Mahowald theorem

Abstract

The Whitney-Mahowald theorem gave normal Euler number ( mod 4 ) (\bmod \,4) for embeddings of a closed 2 n 2n -manifold in Euclidean 4 n 4n -space. We generalize this theorem to embeddings of closed 2 n 2n -manifolds in an oriented 4 n 4n -manifold with an approach in the framework of unoriented bordism groups of maps.